The former Stoke boss heads the betting at 7/4 followed by Martin O'Neill (6/1), Nigel Clough (10/1) and Roberto Di Matteo (16/1), having also previously been the early favourite for the Derby job.
Mowbray was relieved of his position following Saturday's 3-2 defeat at Barnsley, which left Boro with a solitary win in their last 10 games and saw their Sky Bet Championship relegation odds cut to 6/1.
Sky Bet Football Trader Chris Spicer said: "Tony Pulis is the natural favourite for any Championship vacancy given his record of transforming Stoke into a solid Premier League outfit, but it remains to be seen whether he would be a popular choice among the fans given his brand of football.
"We installed him as the 5/2 favourite initially and have cut his price slightly to 7/4 as he attracts more money than any of the other candidates on our list."
Odds subject to change.