Spurs boss Mauricio Pochettino is eager to boost his firepower and would welcome Remy's signing.
The Sun says Tottenham are offering Michael Dawson as part of a new offer for the France international.
Remy was due to sign for Liverpool last month, only for the move to collapse due to a failed medical.
“I sat down with him but I didn’t have to persuade him. He said he’s back and wants to play. Unless [the chance to play in the] Champions League or something massive for him comes up he would like to stay here and play."
For the big stories and the banter follow us on Twitter: @tribalfootball