Tottenham Hotspur have won their first two matches in the Champions League this season.
Manchester United are said to be lining up a £50 million bid for the left-back, who reportedly wants out of Spurs.
Rose put out a controversial statement during the summer, suggesting that he deserved more money.
Although the England international has apologised for his comments, Rose is still said to be keen to earn a pay-rise by moving away from Tottenham.
The Sun claim that United may have a chance of landing Rose if Tottenham go out of the Champions League.
But if Spurs stay in, Mauricio Pochettino is said to want to keep the bulk of his squad together.
Tottenham have won their first two matches in Europe this season, which puts them in a commanding position in their group.
Tottenham’s next two matches in the European competition come against Real Madrid.