I learned this from "The Secret Footballer": most players will say they are keen to stay at a club even if it's not the truth. When they leave and sign a new contract elsewhere, they get paid out the remainder of their old contract (or a lower settlement fee if one can be agreed). If they claim they aren't happy and want to leave, or if they hand in a transfer request, they are not eligible for that pay-out when they leave, so most agents will tell their players to say they're happy in public so they can secure that extra cash in amongst the upcoming transfer.
Ridiculous but true...
I'm not suggesting that Fabregas was definitely lying, just saying that it is possible and this would be the reason.
Thanks for clearing that up
Totally makes sense to some of the bizarre "I want to stay" and the following week they have been signed sealed and delivered to another club.