The left-back, who has also been linked with Manchester United and Inter Milan in recent days, has emerged as a target for antonio Conte, with Chelsea's bid for Juventus wing-back Alex Sandro having hit the buffers.
Before signing Benjamin Mendy from Monaco, Pep Guardiola's Manchester City were also linked with rose, though that interest is believed to have been shelved.
'TMW' reports that Antonio Conte has been in touch with Chelsea owner Roman Abramovich to ask the Russian to do a deal for the England international, with Conte desperate for reinforcements ahead of the new season.
However, English publication 'The Daily Mail' reports that Spurs are not open to bids for the player and that any offers for the 27-year-old will be rejected out of hand.
Rose is currently sidelined through injury and will miss the start of Tottenham's Premier League campaign.