I‘ve multiple version of gcc installed on my systems as follows:

ls -l /usr/bin/gcc*
lrwxrwxrwx 1 root root 7 Jan 11 05:20 /usr/bin/gcc -> gcc-4.4
-rwxr-xr-x 1 root root 239528 Sep 21 2010 /usr/bin/gcc-4.3
-rwxr-xr-x 1 root root 255536 Nov 15 2010 /usr/bin/gcc-4.4

I need to build a nvidia device driver using the same version of GNU compiler as was used to compile the currently running kernel. How do I find out the version of my GNU gcc compiler that was used by upstream Linux distribution to compile and pack my binary Linux kernel?

You need to cat the /proc/version file. This file identifies the kernel version that is currently running and gcc version used to build the kernel.

Sample Outputs From Debian GNU/Linux 6.x

Open a command-line terminal (select Applications > Accessories > Terminal), and then type:
$ cat /proc/version
Sample outputs:

Linux version 2.6.32-5-amd64 (Debian 2.6.32-41) ([email protected]) (gcc version 4.3.5 (Debian 4.3.5-4) ) #1 SMP Mon Jan 16 16:22:28 UTC 2012

Sample Outputs From CentOS / RHEL 6.x Server

Type the following command:
$ cat /proc/version
Sample outputs:

Linux version 2.6.32-220.2.1.el6.x86_64 ([email protected]) (gcc version 4.4.6 20110731 (Red Hat 4.4.6-3) (GCC) ) #1 SMP Tue Dec 13 16:21:34 EST 2011

How Do I Force make To Use Particular Compiler?

You need to set shell environment variable called CC to point to your C compiler. In this example set CC to gcc version 4.3.x:
$ export CC=/usr/bin/gcc-4.3
$ make
OR start building NVIDIA module using gcc-4.3:
$ export CC=/usr/bin/gcc-4.3
$ bash NVIDIA-Linux-x86_64-295.20.run