Of course anything is possible if you throw enough money at it, but physically relocating the station to a larger alternative site would both be expensive, and move the rail link further from the terminals. Also, neither option is going to happen until HS2 comes along, because if you're going to rebuild then also integrate.I think that those operating Manchester Airport would not be too happy at having fewer trains to what is a British top-three airport. There are already vast amounts of adjacent land to the airport that are covered with airport car parking facilities.
All of which means that train length is limited by platform length at the airport which, by extension, means 2 or 3 car trains are needed at Northern, hence 195s.