The 31-year-old is on trial at Sixfields after being released by Oxford and put in an impressive 90 minutes in the 1-1 draw with Histon on Tuesday night.
Willmott made over 100 appearances for the club in a previous spell - his last game coming in a play-off defeat to Southend in May 2005 - and is keen on a return.
He said: "I'd be very happy to sign here again, it really would be ideal for me.
"I like to think I've still got plenty to offer the team but we'll have to wait and see what happens.
"I played quite a few games for Oxford last season and I was a bit surprised to leave, but the manager had his own ideas and that's football."