Remy has scored 12 goals in 29 appearances for club and country this season, and the France international had been attracting plenty of interest in the run-up to the deadline.
Harry Redknapp revealed early last month that he was keen on the 25-year-old, and made a trip to the Stade Velodrome to run the rule over the former Nice star.
The Spurs manager stated that he had been interested in Remy for a number of years, although did not reveal whether or not a formal approach to bring him to White Hart Lane had been made.
However, according to Marseille supremo Vincent Labrune, he rejected a substantial offer from Spurs - a bid he does not believe any other club in Ligue 1 would have resisted.
"In January, I have two deals to manage," Labrune told French newspaper L'Equipe.
"That of Lucho [Gonzalez], who wanted to leave, and that of Remy, who Tottenham wanted to sign.
"I do not think any other president in France would have refused the enormous proposal the London club made."