The Sun is reporting that Tottenham are still reluctant to sell the 27-year-old Rose, but they could be tempted into doing business if Shaw is included as part of the deal.
Manchester United have long been linked with a move to sign Rose and he was touted as a target for the Red Devils last year, but a move failed to materialise.
Rose has struggled for both form and fitness this season and has only made seven Premier League starts for the north London side.
According to the same story, Shaw looks “certain” to leave Manchester United this summer after an alleged training ground bust-up with Jose Mourinho.
Spurs boss Mauricio Pochettino knows Shaw well after having worked with him during the pair’s spell together at Southampton.
Manchester United are likely to be on the lookout for a number of new signings this summer as Mourinho looks to strengthen his squad and assemble a team capable of winning the Premier League next season.
The Red Devils host Arsenal in the Premier League at Old Trafford on Sunday.
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