diff --git a/tools/docs/test_doc_build.py b/tools/docs/test_doc_build.py
index 47b4606569f9..4082317d581d 100755
--- a/tools/docs/test_doc_build.py
+++ b/tools/docs/test_doc_build.py
@@ -11,29 +11,47 @@ and optionally test the build.
 
 import argparse
 import asyncio
+import glob
 import os.path
-import shutil
+import re
 import sys
 import time
 import subprocess
 
-# Minimal python version supported by the building system.
+MIN_PYTHON_SUBVER = 9  # Currently, Python 3.9 is the minimal supported version
 
-PYTHON = os.path.basename(sys.executable)
+RE_VERSION = re.compile(r"python3\.\d+$")
 
-min_python_bin = None
 
-for i in range(9, 13):
-    p = f"python3.{i}"
-    if shutil.which(p):
-        min_python_bin = p
-        break
+def get_min_python_bin(min_subver):
+    """Get minimal python binary since 3.MIN_PYTHON_SUBVER"""
+    bins = set()
 
-if not min_python_bin:
-    min_python_bin = PYTHON
+    paths = os.environ.get("PATH", "").split(os.pathsep)
+    for d in paths:
+        for p in glob.glob(os.path.join(d, "python3.[0-9]*")):
+            if not RE_VERSION.search(p):
+                continue
 
-# Starting from 8.0, Python 3.9 is not supported anymore.
-PYTHON_VER_CHANGES = {(8, 0, 0): PYTHON}
+            ver = int(p.split(".")[1])
+            if ver < min_subver:
+                continue
+
+            if os.path.isfile(p) and os.access(p, os.X_OK):
+                bins.add(p)
+
+    if not bins:
+        return None
+
+    return sorted(bins, key=lambda x: (3, int(x.split(".")[1])))[0]
+
+# Minimal python versions. Please notice that for 3.4.3, older python
+# versions would work with Sphinx, but kernel doc build is not compatible
+# with them anymore, due to Sphinx extensions and kernel-doc.
+PYTHON_VER_CHANGES = {
+    (3, 4, 3): (3, MIN_PYTHON_SUBVER),
+    (8, 0, 0): (3, 10),
+}
 
 DEFAULT_VERSIONS_TO_TEST = [
     (3, 4, 3),   # Minimal supported version
@@ -173,7 +191,7 @@ class AsyncCommands:
         self.output = None
         self.fp = fp
 
-    def log(self, out, verbose, is_info=True):
+    def log(self, out, verbose=True, is_info=True):
         out = out.removesuffix('\n')
 
         if verbose:
@@ -362,8 +380,19 @@ class SphinxVenv:
             if not args.verbose:
                 args.verbose = True
 
+        cmd = AsyncCommands(fp)
+
         cur_requirements = {}
-        python_bin = min_python_bin
+        python_bin = get_min_python_bin(MIN_PYTHON_SUBVER)
+        if not python_bin:
+            python_bin = os.path.basename(sys.executable)
+            python_ver = tuple(sys.version_info[:2])
+
+            if python_ver < (3, MIN_PYTHON_SUBVER):
+                sys.exit(f"Python {python_ver[0]}.{python_ver[1]} is too old.")
+        else:
+            ver = int(python_bin.split(".")[1])
+            python_ver = tuple([3, ver])
 
         vers = set(SPHINX_REQUIREMENTS.keys()) | set(args.versions)
 
@@ -372,8 +401,14 @@ class SphinxVenv:
                 new_reqs = SPHINX_REQUIREMENTS[cur_ver]
                 cur_requirements.update(new_reqs)
 
-            if cur_ver in PYTHON_VER_CHANGES:          # pylint: disable=R1715
-                python_bin = PYTHON_VER_CHANGES[cur_ver]
+            if cur_ver in PYTHON_VER_CHANGES:
+                new_ver = PYTHON_VER_CHANGES[cur_ver]
+                if python_ver < new_ver:
+                    python_bin = get_min_python_bin(new_ver[1])
+
+                    if not python_bin:
+                        cmd.log(f"Can't check {cur_ver}: {python_bin} not found.")
+                        break
 
             if cur_ver not in args.versions:
                 continue
@@ -390,7 +425,6 @@ class SphinxVenv:
                                        python_bin)
 
         if args.build:
-            cmd = AsyncCommands(fp)
             cmd.log("\nSummary:", verbose=True)
             for ver, elapsed_time in sorted(self.built_time.items()):
                 cmd.log(f"\tSphinx {ver} elapsed time: {elapsed_time}",