With most recent 3.10 (v3.10.2-169-g98e2ee60) I call

./configure --prefix=/  && make && make DESTDIR=/home/d/A install

It fails with:

running build
running build_ext
INFO: Can't locate Tcl/Tk libs and/or headers

Python build finished successfully!
The necessary bits to build these optional modules were not found:
_gdbm                 _tkinter              nis                
readline                                                       
To find the necessary bits, look in setup.py in detect_modules() for the module's name.


The following modules found by detect_modules() in setup.py, have been
built by the Makefile instead, as configured by the Setup files:
_abc                  pwd                   time               

running build_scripts
copying and adjusting /git/cpython/Tools/scripts/pydoc3 -> build/scripts-3.10
copying and adjusting /git/cpython/Tools/scripts/idle3 -> build/scripts-3.10
copying and adjusting /git/cpython/Tools/scripts/2to3 -> build/scripts-3.10
changing mode of build/scripts-3.10/pydoc3 from 644 to 755
changing mode of build/scripts-3.10/idle3 from 644 to 755
changing mode of build/scripts-3.10/2to3 from 644 to 755
renaming build/scripts-3.10/pydoc3 to build/scripts-3.10/pydoc3.10
renaming build/scripts-3.10/idle3 to build/scripts-3.10/idle3.10
renaming build/scripts-3.10/2to3 to build/scripts-3.10/2to3-3.10
running install_lib
creating /lib/python3.10/lib-dynload
error: could not create '/lib/python3.10/lib-dynload': Permission denied
make: *** [Makefile:1761: sharedinstall] Error 1