Rose suffered a knee injury in January and has endured a frustrating spell on the sidelines with multiple setbacks in that time, but he finally appears to be nearing a comeback.
However, United will face stiff competition for the 27-year-old's signature as the newspaper says Chelsea are also interested in signing Rose when the transfer window re-opens this winter. Spurs will not want to lose Rose, but they have a ready-made replacement in Ben Davies, who is only a notch or two below the England worldwide in an attacking sense, and offers greater reliability in defence.
Lamela has not played for Tottenham for nearly a year because of hip problems and even spent time at former club Roma as he attempted to overcome his injuries before undergoing surgery.
Rose was in the form of his life last season when he damaged the medial ligament in his left knee during Spurs' 0-0 draw at Sunderland on 31 January. But after five months of rehabilitation he returned to first-team training this week and is understood to be feeling good.
It is believed that this Premier League and worldwide footballer wants a move to Jose Mourinho's Manchester United.
Lamela has been missing for even longer, having picked up a hip problem that has prevented him from playing since October 25 previous year.
While Danny Rose is only just returning from injury the news is still not great for Spurs fans.