Spurs have not made a move for the Colombian striker this month.
The striker has struggled for his best form since a big-money move from Porto to Atletico Madrid in La Liga in the summer and Spurs were said to have bid £22.8 million for the striker - as their pursuit of Saido Berahino appears to be falling away.
However a report in the Daily Mail has now stated that Spurs have not made any bid for the player.
It is instead believed that Spurs will wait until the end of the transfer window to see if they can snap up the striker at a lower price.
Tottenham have already had successful negotiations with Atletico recently - with Toby Alderweireld making a move to White Hart Lane from the Spanish capital in the summer.
Spurs need a striker to help their assault on domestic and European football with Harry Kane their only currently fully-fit attacking option - with Clinton N'Jie injured and Son Heung-min more of an attacking midfield option.
So it will be interesting to see whether Spurs do make a move for Martinez this window, or indeed another striker, whilst Berahino interest is not going to dissipate anytime soon.