Spurs have money to spend in the final 48 hours of the transfer window after agreeing a deal earlier in the week to sell Luka Modric to Real Madrid.
The signing of Moussa Dembele from Fulham has already been completed and it is understood attention has now turned to bringing in Remy.
The 25-year-old has emerged as a target despite Andre Villas-Boas declaring last week that he was happy with his striking options.
Emmanuel Adebayor has signed a permanent contract at White Hart Lane this summer and Jermain Defoe remains a key part of Villas-Boas' plans, but it seems Remy could now be set to come in and provide further competition. Remy has been linked with a move to the Premier League in the past after attracting interest with a series of impressive performances in Ligue 1.
He has been with Marseille since August 2010, having previously had stints with Lyon, Lens and Nice.