Previous boss Stale Solbakken told Hunt that he could move elsewhere if an offer materialised but the Waterford man has been out since October with a hip injury that required surgery. The change at the top has opened a window of opportunity at Molineux, with Saunders speaking as though the Irish international is part of his plans. The 31-year-old is out of contract in the summer.
" Stephen Hunt is a player that I am looking forward to working with," said Saunders. "I spoke to him on Tuesday and said 'let's see if we can get you fit.'
"I have brought in Mal Purchase with me to go down that route – strengthening and conditioning. I will be turning Mal towards Stephen and seeing if he can work some wonders and get him on the pitch with us. He can just run so we will have to see how his progress takes him.
"He is another player of Premier League quality who has a good attitude. We know that he is good enough."
Saunders has no doubts about Doyle's credentials either, and identified his performance in training as one of the positives of his first week in the job.
The Wexford man has scored just five goals this term, but he has often been deployed in a deeper role and the new boss also thinks that the 29-year-old could do with better support from those around him.
"I've watched Kevin in training and he's been brilliant the last three days," said Saunders. "On Tuesday, he was unplayable and he had a right battle with a couple of the young centre-backs. That shows me he wants to do it.
"I think the goals will come for him. If I am picking a player and I know I am going to get the maximum he has got, then you sleep better before the game – and that is what Kevin Doyle gives me.
"Those are the kind of players that you want around you. We need a few more like Kevin. He has to get the right service and probably he has not been getting the ball quickly enough. There are things I can teach him and pass on. You can't give anyone an instinct.
"Every season I played I went eight or nine games without scoring but I managed to stay in the team because the manager thought I was working hard and I brought something else to the table."
Nevertheless, Saunders has pinpointed a striker as one of his January targets, with the Welshman confident that a play-off charge is still possible.
Doyle has been linked with a move away in the last three transfer windows, and is unlikely to fancy another year at Championship level if they fail to make the late burst that Saunders is predicting.