I was having the same problem. None of the above solutions worked for me. The key challenge was that I didn't have the root access. So, I first download the source of libffi. Then I compiled it with usual commands:
./configure --prefix=desired_installation_path_to_libffi
make
Then I recompiled python using
./configure --prefix=/home/user123/Softwares/Python/installation3/ LDFLAGS='-L/home/user123/Softwares/library/libffi/installation/lib64'
make
make install
In my case, 'home/user123/Softwares/library/libffi/installation/lib64' is path to LIBFFI installation directory where libffi.so is located. And, /home/user123/Softwares/Python/installation3/ is path to Python installation directory. Modify them as per your case.