MANCHESTER, United Kingdom — Manchester United took time off from their pursuit of Arsenal forward Alexis Sanchez to coast to a comfortable 3-0 victory against Stoke at Old Trafford on Monday. Antonio Valencia and Anthony Martial in the first half, and Romelu Lukaku after the break, were on the scoresheet as Jose Mourinho finally beat struggling Stoke as United manager at the fourth time of asking. But this performance, and numerous missed chances, still provided Mourinho with plenty of evidence that he needs to add Arsenal’s Sanchez to his squad during the January transfer window, despite cutting neighbours Manchester City’s lead at the top of the Premier League to 12 points. United believe they have won the battle for the 35 million pound-rated player, who is out of contract with Arsenal at the end of the season, especially after rivals City let the Gunners know on Monday that they are no longer interested in Sanchez, given his fee and salary demands. New Stoke manager Paul Lambert, appointed on the morning of this game, was watching from the stands before officially starting work today and must have been unimpressed as United raced into an early lead through Valencia, back in the…