It is possible but some cats will go balistic! If and when you move you will be able to decide as you will have to keep your cats in for a period of time anyway....If in this period of time if Monkey has not lost the urge and you view the new area to be safe then work away...
I would suggest if this is not a ground floor flat or one that has not got easy access for the cat to get back in to try and lovingly persuade your cat to stay indoors.....
I have 2 cats taken off the streets who would not thank you if you went to put them outside...When I lived in a diff area My Baz and Yagga used to go out until Baz decided to get himself trapped in a lock-up for 13 days....Well much to his disapproval he is now as are all my bunch indoor/outdoor catproofed garden....he has finally given in....
Good Luck in whatever you decide!
