Watford have announced the signing of Italy international Marco Motta, subject to international clearance.
Mark Noble has signed a new deal with West Ham which will keep him at the club until the summer of 2020.
The 34-year-old, who was released by Cardiff City at the end of last season, has been working with Warburton’s squad for the past few days.
He has previously played for Queens Park Rangers, Sunderland, Derby County and Watford, and Warburton does not think it would be a problem for a club so dedicated to developing young talent to have a player of Smith’s experience on their books.
“I've known Tommy since we were both at Watford and I know just how good he is. We are having a look at him, and he is having a look at us,” said Warburton in Get West London.
“He is a model pro who looks after himself and is still unbelievably fit. He wouldn't still be with us if we were going to rule him out due to his age.
“We have some very talented young players at this club, but especially moving up a level, you need to make sure you have some wise old heads too.”
Warburton is still looking to bring in a couple more players before the Championship campaign kicks off and has been linked with a move for Rochdale striker Scott Hogan, although he is reluctant to discuss specific targets.
He said: “We hope to have one or two more in by the start of the season, and we are making good progress on the striker front.
“Ideally you'd like all your signings in place by the end of June, but you have to be patient, and if you rush things, sometimes you miss out.”