The Clarets have added an extra attacking dimension to their game this season, but it may not be on full display against United.
The Red Devils boss has been heavily linked with a move for a left-back this month - Danny Rose, Ryan Sessegnon and Kieran Tierney have emerged as targets - but Shaw has made a significant impression on Mourinho recently.
With Jose Mourinho set for a contract extension, Paul Mariner and Alexis Nunes debate whether his tenure at Man United will be the defining moment of his career.
It may not have been vintage United but after leaders Manchester City lost their unbeaten league record in a 4-3 reverse at Liverpool on Sunday, it was vital Jose Mourinho's side took the chance to close the gap at the top to 12 points.
Shaw, 22, was criticised last season by Mourinho, who said the defender was "a long way behind" his teammates but he has now started United's last five games, his best run in the team since August 2016.
However, Shaw has now completed 90 minutes in six matches in the space of a month, and Mourinho has claimed that there are few better left-backs than the England global.
'He has played very well.
Bojan could be set for an early return to Stoke City, with claims from the Stoke Sentinel that the attacker wants to return early from his loan spell at Alaves in a bid to help the club fight relegation.
Ahead of the weekend's action, Zlatan Ibrahimovic and Eric Bailly remain sidelined for United, while Daley Blind will also miss the fixture with a "small problem".
United now sit 12 points behind their local rivals in the Premier League table but there is certainly a feeling that the Manchester giants have been improving under the tutelage of Mourinho.
Rob is ESPN FC's Manchester United correspondent.