The France international was overlooked in Jose Mourinho's matchday squad for Manchester United's 1-1 draw at Stoke on Saturday.
The Daily Mail claim Mourinho was unhappy with Martial's performance against Liverpool and that the Frenchman was upset to have been completely dropped.
Bookmakers back Anthony Martial to leave Manchester United
And bookmakers Ladbrokes have responded by slashing Martial's odds to leave the club in the January window to just 7/4.
Should the 20-year-old remain at Old Trafford until the end of the season, it's 5/4 that Mourinho offloads him in the summer.
A Ladbrokes spokesman said: “There's been a simmering tension been Jose and Martial all season, but after being dropped at Stoke, the Frenchman is nearer the exit than ever before.”
Jose Mourinho dropped Anthony Martial from his matchday squad against Stoke
Manchester United fans react on Twitter to starting XI against Stoke City
Sat, January 21, 2017
Manchester United fans react on Twitter as Jose Mourinho leaves out Anthony Martial and Michael Carrick for the Red Devils' clash with Stoke City
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Manchester United fans react as Anthony Martial and Michael Carrick are left out of the starting XI against Stoke City
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Martial signed for United in the summer of 2015 and enjoyed a stunning debut campaign – scoring 20 goals and providing 16 assists – but has struggled to hold onto a first-team spot this term.
His Old Trafford team-mate Ashley Young has also been linked with a move away this month, with West Brom (5/4), Watford (8/1), Everton (10/1), Stoke (14/1) and Aston Villa (16/1) all in the running to take him on loan.