Normally if you formally give notice it is very difficult to stay in the flat.
The landlord does not have any legal obligation to extend your lease because you terminated the lease agreement with the 31 January and they have no obligation to provide you with accommodation after that date.
Having said that, everything in life is potentially negotiable, so give it a try. For legal advice on this issue you can contact ASLOCA (or whatever it is called Zurich). Ah, here it is:
http://www.mieterverband.ch/