Stewart is in temporary charge after Ian McCall left last week for Partick Thistle and has already overseen a 3-0 win at Arbroath to keep Ayr joint top of the Ladbrokes Championship.
Forrest says the dressing room is fully behind the former Airdrie manager getting the job full-time.
The winger, who has been named Ladbrokes Player of the Month for September, said: “I hope he gets the job. I think all the boys would say the same because we all get on well with him.
“He’s managed before and he’s got great experience from his time in England so I think it would be ideal for us if he was to get it.
“The gaffer had done a great job at Ayr and everything was going so well and then suddenly he’s gone.
“Everything happened so quick that we hardly had time to think about it. And the good thing was we had Sandy here who has been a main man anyway and doing most of the training. So although Ian McCall is a big miss, we’ve got someone here who can take us on.
“It was a bit weird not seeing the gaffer and he has been a great help to me in terms of my development so I have a lot to thank him for.”
Forrest hit five goals in three wins in September and his brother, Celtic and Scotland winger James, was one of the first to congratulate him. He added: “The team has done brilliantly – we’ve won every game and I’ve managed to score a few goals so it’s been great for me too. It’s nice for someone else in the Forrest family to get some recognition! James has been exceptional for years now and achieved so much. But he was quick to get in touch to congratulate me so that was nice.”