the cpu is 64-bit. you're mixing up the cpu with the operating system. your operating system is 32-bit which is not the same thing at all. they do not mean the same thing for the system. it's perfectly normal to have a 32-bit windows with a 64-bit processor. we had 64-bit processors long before 64-bit windows became the norm. 64-bit windows was needed to address larger amounts of ram (over 3.5 gb) and a few other things that slowly became the norm for pc's. but again, 32 bit windows on a 64-bit cpu is perfectly normal and nothing to worry about.
any reason you want to upgrade to 64-bit windows other than thinking you need it with the 64-bit cpu? otherwise if everything works fine and you have less than 4 gb of ram, then it really is not needed.
if you're pc won't install 64-bit windows, it has nothing to do with your cpu but rather likely an issue with the motherboard. what are the full specs of the system? can't really start looking into windows install question with only the cpu known