Paolo Di Canio is keen to sign Rose on a permanent basis this summer, and his future is due to be decided when he returns to pre-season training with Tottenham next month.
The defender is reluctant to remain with Spurs if he is behind Assou-Ekotto and Kyle Naughton in the pecking order, and Sunderland could offer a firm guarantee of regular first-team football next season.
However, Spurs boss Andre Villas-Boas has decided to cash in on Assou-Ekotto, with Rose now regarded as a better long-term bet for the left-back berth.