The 22-year-old, who made four appearances for the Team GB Olympic team this summer and can also play at left-back, is behind the likes of Gareth Bale and Benoit Assou-Ekotto in the pecking order for places at White Hart Lane.
|10/1||Tottenham are 10/1 with Bet365 to win the League Cup
The development comes after the Black Cats boss revealed on Monday that Kieran Richardson, who is similarly positionally versatile to Rose, has asked to leave the club.
The Tottenham youngster has made 29 first-team appearances for his side, scoring one goal, as well as several loan spells in lower divisions but looks likely to get more game time under O'Neill.
Sunderland, who drew their opening fixture of the Premier League season 0-0 against Arsenal, are also close to signing Manchester City misfit Adam Johnson for £11 million.