Shaw joined United in a £30million deal three years ago from Southampton, but his time at Old Trafford has been plagued by injuries.
Added to that, he has failed to convince Jose Mourinho of his ability when fit.
Tottenham meanwhile, managed to fend off United and Manchester City over the summer to keep hold of Rose, who only returned to action in midweek in the Carabao Cup against West Ham after recovering from a long-term knee injury.
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Luke Shaw and Danny Rose could both be on the move
They might as well do the swap now. Shaw is loved by Mauricio Pochettino
Tim Sherwood
Other reports over the summer suggested United and Tottenham were exploring a swap deal involving Rose and Shaw.
And Sherwood thinks it would be a deal that would suit both parties.
“I think in the left-back area, Blind has been more of a regular," Sherwood told Sky Sports' The Debate Show.
“It’s the position where Mourinho is most unsure.
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Tim Sherwood thinks Manchester United and Tottenham should do a swap deal
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“They might as well do the swap now. Shaw is loved by Mauricio Pochettino.
“Danny [Rose] is loved by Mourinho.
“Just do the swap now and get it over and done with.”
United and Tottenham meet today at Old Trafford (12.30pm), with both desperate for a victory to keep up the pressure on Premier League leaders City.
