City face a crucial week in their quest to end a 35-year trophy drought.
They travel to Ukraine on Wednesday ahead of the Europa League last 16 first leg meeting with Dynamo Kiev on Thursday. Then on Sunday Roberto Mancini's side have a home FA Cup quarter-final tie against Reading.
Former City boss Keegan said: "I think they will win something this year, it might be the FA Cup, it might be the Europa League. The sooner you get a trophy, the quicker the pressure comes off. A lot of money is being spent, so you must win things.
"It doesn't make your job any easier just because someone gives you a lorry load of money. It just means you have a chance of winning something. The pressure is greater because of that.
"Once you win one thing, others come along. The first cup is like a magnet, it seems to attract all the other trophies. I am delighted for them."