Think carefully about what you want to do.
Don't sign a new lease on another property, until you have received formal notice to vacate. That is, if you agree to vacate early and the LL has given you 1 month's notice to vacate...and you've agreed the terms of the early termination of the lease....
From, the LL's point of view, everything is subject to the proposed buyer, who may or may not buy, or any future prospective buyers.
Be wary of what the LL actually wants, because if they don't actually give you a formal ONE months Notice to Vacate, your tenancy would still continue to run until February.
The best thing is to actually agree a termination date, with compensation to you.
Make sure anything you agree is written and signed by both parties.