As reported by the Manchester Evening News, their sources state that Spurs chairman Daniel Levy did contact the Red Devils over the possibility of signing the duo, although he was swiftly rebuffed as the club failed to make a signing this summer.
The pair are somewhat on the periphery of Jose Mourinho's plans at Old Trafford, with Mata and Martial getting hooked at 45 and 60 minutes respectively during the recent 3-2 defeat away to Brighton.
Martial especially had been linked with a number of clubs over the course of the recent transfer window, with Tottenham being one of those sides rumoured to be interested, while the Spaniard was apparently being courted by former club Valencia.
Despite the perceived struggles for both Mata and Martial, it would've been highly unlikely to see Mourinho sell both players to direct rivals in the Premier League, which is perhaps why Tottenham's supposed interest was immediately quashed.
The two clubs were also reportedly in discussions over the transfer of Belgian centre back Toby Alderweireld on deadline day, although the move failed to materialise as Mourinho missed out on a number of reported central defensive targets.
Tottenham are set to face Manchester United at Old Trafford on Monday, as Mauricio Pochettino looks to make it three wins from three, while Mourinho will be hoping to see a reaction after a poor showing from his side against Brighton a week ago.