The Yorkshire-born 27-year-old, who has been sidelined with a knee injury for six months, has been linked with a move to Manchester United and Chelsea this summer.
Tottenham have not made a major signing during the transfer window and have seen Rose's fellow full-back Kyle Walker join Premier League title rivals Manchester City.
Rose, who has a contract until 2021 with Spurs, stressed he was not looking to leave just yet, but would discuss a potential move with the club if an offer came in.
"I am reaching my peak and have probably only got one big contract left in me," the England defender told the Sun. "Time is running out and I do want to win trophies. I don't want to play football for 15 years and not have one trophy or one medal.
"I will say this too, I will play up north. I don't know exactly when but I will get back up north and play some football somewhere. I have been away for over 10 years now and I don't get to see my mum that often.
"I'm not saying I want out, but if something came to me that was concrete, I'd have no qualms about voicing my opinions to anyone at the club."