I would suggest to buy parts and do the whole build from the ground up.
When it comes to your question, some workspace prebuilts dont allow you to take out your current processor so i dont even know if thats possible, it might be but you'd be better off buying a new system imo.
However if you can take the cpu out, your options are very limited and wont get you very far with the gaming aspect of things. Furthest and best cpu you can go to is for an E6850, which is not very good either but if you want to play low demanding games with not the best fps go for it.