Following newspaper reports of unrest at The Hawthorns, bookmakers saw a gamble on Mel leaving his post, with Sky Bet going into 10/11 (from 5/2) in their 'sack race' betting on Wednesday morning.
The former Real Betis coach was only appointed on January 9 but has failed to lead the Baggies to a victory during his seven games in charge and they remain in the tick of the relegation battle.
Sky Bet's head of football trading Paul Wiggins said: "We saw a consistent flow of bets on Mel to go after a couple of national newspapers suggested he was fighting to save his job.
Mel was brought in to replace Steve Clarke who was ditched after a poor start to the season.
West Brom finished eighth last term but are currently 17th, just one point outside the relegation zone.
Their next game is at home to Manchester United on March 8, while crunch games against relegation rivals Swansea, Hull, Cardiff and Norwich are also looming next month.
The Baggies are currently 11/4 with Sky Bet to be relegated.