Spurs were keen to sign Martial back during his time at Monaco.
And the Daily Mirror claim they are ready to go after the France international again at the end of the season.
Despite scoring 17 goals under Louis van Gaal last term, Martial has found life at Old Trafford tough under Jose Mourinho.
The former Chelsea boss has regularly criticised him and the 21-year-old could be off in the summer.
Anthony Martial could leave Manchester United for Tottenham
Five most likely summer deals according to the bookies
Wed, February 1, 2017
Express Sport takes a look at the five most likely deals that could happen this summer. Odds provided by BetStars
1 of 5
Griezmann to the Premier League – Man Utd 15/8, Chelsea 6/1, Man City 8/1
Yaya Sanogo looks set to leave Arsenal at the end of the season
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Arsenal have reportedly decided to offload Yaya Sanogo at the end of the season.
Sanogo is in his fourth season at Arsenal since signing from Auxerre in 2013.
The Frenchman has toiled in north London, scoring just a solitary Premier League goal.
And the Daily Mail say the striker will leave in the summer.
Sanogo's contract expires at the end of the season and Arsenal will let him go for free, with Saint Etienne in the race to sign him.
Manchester City want to sign Lucas Hernandez – and his brother Theo
City have been impressed with both brothers this season.
Lucas has broken into Atletico's staring XI to provide competition for Jose Giminez and Diego Godin.
Theo, meanwhile, has starred on loan at La Liga side Alaves.
It is claimed City are prepared to spend £40million on the siblings while Atletico could be tempted if Sergio Aguero is included as part of a deal.