diff --git a/packages/eslint-plugin/src/rules/no-require-imports.ts b/packages/eslint-plugin/src/rules/no-require-imports.ts
index 9b83ac66aeca..1956694484f4 100644
--- a/packages/eslint-plugin/src/rules/no-require-imports.ts
+++ b/packages/eslint-plugin/src/rules/no-require-imports.ts
@@ -42,16 +42,23 @@ export default util.createRule<Options, MessageIds>({
     function isImportPathAllowed(importPath: string): boolean {
       return allowPatterns.some(pattern => importPath.match(pattern));
     }
+    function isStringOrTemplateLiteral(node: TSESTree.Node): boolean {
+      return (
+        (node.type === AST_NODE_TYPES.Literal &&
+          typeof node.value === 'string') ||
+        node.type === AST_NODE_TYPES.TemplateLiteral
+      );
+    }
+
     return {
       'CallExpression[callee.name="require"]'(
         node: TSESTree.CallExpression,
       ): void {
-        if (
-          node.arguments[0]?.type === AST_NODE_TYPES.Literal &&
-          typeof node.arguments[0].value === 'string' &&
-          isImportPathAllowed(node.arguments[0].value)
-        ) {
-          return;
+        if (node.arguments[0] && isStringOrTemplateLiteral(node.arguments[0])) {
+          const argValue = util.getStaticStringValue(node.arguments[0]);
+          if (typeof argValue === 'string' && isImportPathAllowed(argValue)) {
+            return;
+          }
         }
         const variable = ASTUtils.findVariable(
           context.sourceCode.getScope(node),
@@ -68,12 +75,11 @@ export default util.createRule<Options, MessageIds>({
         }
       },
       TSExternalModuleReference(node): void {
-        if (
-          node.expression.type === AST_NODE_TYPES.Literal &&
-          typeof node.expression.value === 'string' &&
-          isImportPathAllowed(node.expression.value)
-        ) {
-          return;
+        if (isStringOrTemplateLiteral(node.expression)) {
+          const argValue = util.getStaticStringValue(node.expression);
+          if (typeof argValue === 'string' && isImportPathAllowed(argValue)) {
+            return;
+          }
         }
         context.report({
           node,
diff --git a/packages/eslint-plugin/src/rules/no-var-requires.ts b/packages/eslint-plugin/src/rules/no-var-requires.ts
index 30838ed7b99d..9bb9fb7c1921 100644
--- a/packages/eslint-plugin/src/rules/no-var-requires.ts
+++ b/packages/eslint-plugin/src/rules/no-var-requires.ts
@@ -1,7 +1,7 @@
 import type { TSESTree } from '@typescript-eslint/utils';
 import { AST_NODE_TYPES, ASTUtils } from '@typescript-eslint/utils';
 
-import { createRule } from '../util';
+import { createRule, getStaticStringValue } from '../util';
 
 type Options = [
   {
@@ -43,16 +43,24 @@ export default createRule<Options, MessageIds>({
     function isImportPathAllowed(importPath: string): boolean {
       return allowPatterns.some(pattern => importPath.match(pattern));
     }
+
+    function isStringOrTemplateLiteral(node: TSESTree.Node): boolean {
+      return (
+        (node.type === AST_NODE_TYPES.Literal &&
+          typeof node.value === 'string') ||
+        node.type === AST_NODE_TYPES.TemplateLiteral
+      );
+    }
+
     return {
       'CallExpression[callee.name="require"]'(
         node: TSESTree.CallExpression,
       ): void {
-        if (
-          node.arguments[0]?.type === AST_NODE_TYPES.Literal &&
-          typeof node.arguments[0].value === 'string' &&
-          isImportPathAllowed(node.arguments[0].value)
-        ) {
-          return;
+        if (node.arguments[0] && isStringOrTemplateLiteral(node.arguments[0])) {
+          const argValue = getStaticStringValue(node.arguments[0]);
+          if (typeof argValue === 'string' && isImportPathAllowed(argValue)) {
+            return;
+          }
         }
         const parent =
           node.parent.type === AST_NODE_TYPES.ChainExpression
diff --git a/packages/eslint-plugin/tests/rules/no-require-imports.test.ts b/packages/eslint-plugin/tests/rules/no-require-imports.test.ts
index 42374ccffbf8..bdfddbc25ae0 100644
--- a/packages/eslint-plugin/tests/rules/no-require-imports.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-require-imports.test.ts
@@ -31,6 +31,10 @@ require('remark-preset-prettier');
       code: "const pkg = require('../package.json');",
       options: [{ allow: ['/package\\.json$'] }],
     },
+    {
+      code: 'const pkg = require(`./package.json`);',
+      options: [{ allow: ['/package\\.json$'] }],
+    },
     {
       code: "const pkg = require('../packages/package.json');",
       options: [{ allow: ['/package\\.json$'] }],
@@ -47,6 +51,10 @@ require('remark-preset-prettier');
       code: "import pkg = require('some-package');",
       options: [{ allow: ['^some-package$'] }],
     },
+    {
+      code: 'import pkg = require(`some-package`);',
+      options: [{ allow: ['^some-package$'] }],
+    },
   ],
   invalid: [
     {
@@ -156,6 +164,17 @@ var lib5 = require?.('lib5'),
         },
       ],
     },
+    {
+      code: 'const pkg = require(`./package.jsonc`);',
+      options: [{ allow: ['/package\\.json$'] }],
+      errors: [
+        {
+          line: 1,
+          column: 13,
+          messageId: 'noRequireImports',
+        },
+      ],
+    },
     {
       code: "import pkg = require('./package.json');",
       errors: [
@@ -188,5 +207,16 @@ var lib5 = require?.('lib5'),
         },
       ],
     },
+    {
+      code: 'import pkg = require(`./package.json`);',
+      options: [{ allow: ['^some-package$'] }],
+      errors: [
+        {
+          line: 1,
+          column: 14,
+          messageId: 'noRequireImports',
+        },
+      ],
+    },
   ],
 });
diff --git a/packages/eslint-plugin/tests/rules/no-var-requires.test.ts b/packages/eslint-plugin/tests/rules/no-var-requires.test.ts
index 718bcc46db31..2720475b3b8d 100644
--- a/packages/eslint-plugin/tests/rules/no-var-requires.test.ts
+++ b/packages/eslint-plugin/tests/rules/no-var-requires.test.ts
@@ -36,6 +36,10 @@ const json = require('./some.json');
       code: "const pkg = require('some-package');",
       options: [{ allow: ['^some-package$'] }],
     },
+    {
+      code: 'const pkg = require(`some-package`);',
+      options: [{ allow: ['^some-package$'] }],
+    },
   ],
   invalid: [
     {
@@ -209,5 +213,16 @@ configValidator.addSchema(require('./a.json'));
         },
       ],
     },
+    {
+      code: 'const pkg = require(`./package.json`);',
+      options: [{ allow: ['^some-package$'] }],
+      errors: [
+        {
+          line: 1,
+          column: 13,
+          messageId: 'noVarReqs',
+        },
+      ],
+    },
   ],
 });