If it were me, I'd be keeping quiet about it. As long as you know you can tide yourself over until your next job starts. I'd be worried that you might spook anyone during the buying process which could make it flop.
I tend to take risks. You need to evaluate what could potentially go wrong, and then how likely these things are to happen. I took some risks with the source of my deposit money (which I can't discuss here). I needed to, or I'd still be renting now.
If it were me, I'd be keeping quiet about it. As long as you know you can tide yourself over until your next job starts. I'd be worried that you might spook anyone during the buying process which could make it flop.