The report has also claimed that the England international defender would consider a move to Manchester United, but the Red Devils are not expected to make an offer for him this month.
Tottenham, though, do not want to sell Rose this summer, claims the report in The Times.
The report follows an interview from Rose to The Sun in which he suggested that he would be open to the idea of leaving Tottenham and urged the North London club to sign two or three world-class players.
"I think that is the biggest thing as a player, you see your own game improving, you are moving in the right direction, you are challenging for trophies all of a sudden,” Jenas told Goal.com. “That makes you stay. I think that’s what’s happened with these players.
"In saying that, one or two might leave in the next couple of seasons. I think essentially, they as a club as players, certainly the ones I have spoken to, the majority of them are happy.”