Can car keys be re-programmed?

Hey guys quick story. So I currently have a 2001 audi a4 2.8. Recently the transmissions has been slipping due to a leak from a seal close to the torque converter. A mechanic is telling me that it'll apparently cost close to $3000 to get it fixed. So while driving with my brother we see another a4 (1.8) same year and everything the only other difference is that mine is a auto and this one is a manual. The owner even said hes just trying to get rid of it. The problem is that he said he lost the keys and doesnt know where it is, which is why the car is just sitting there. So what I want to know is, is there anyway i can get my car reprogrammed to work with his a4 instead of mine.