The report continues by saying that Rose has recently pondered whether he will be able to win trophies at Spurs as he has bold ambitions for his future.
But, the race for Rose is set to heat up with Chelsea also entering the race as Antonio Conte seeks to strengthen the left wing-back area.
Indeed, after the departure of Walker manager Mauricio Pochettino will no want to lose his other starting full-back.
Tottenham have no interest in selling Rose this summer with the club instead focused on signing new recruits.
At the same time, this new Rose to Chelsea story reflects how the Blues have been stonewalled in the transfer market.
The Evening Standard claim that Rose is happy to have been linked with a move.
Alex Oxlade-Chamberlain, another North Londoner not heading for the Potteries despite one recent report, is clearly in a mischievous mood.
Tottenham will be starting the season with Ben Davies in the left-back position because of Rose's knee injury. Rose would be a potent addition and would boost the Home Grown quota for the club as well.
Spurs are under no pressure to sell as Rose only signed a new five-year contract worth £70,000-a-week last summer but the player could make life difficult as he knows he would receive a significant pay-rise if he moved to Old Trafford.
The 27-year-old was out injured until now, which is why Tottenham didn't get many enquiries for the player.
The Tottenham left-back has enjoyed an excellent couple of seasons at White Hart Lane, leading to speculation that he might move on.