And Mourinho has made no secret that he is a fan of the Mexican striker. The Belgian poacher has had seen an ordinary second half of the season after kick-starting things in style for the Old Trafford outfit.
The deal may also make sense for Arsenal, but Sanchez appears determined to move to City, and it may be hard to persuade the Chile global his future lies anywhere other than the Etihad Stadium.
The report suggests that Leicester's Vardy would cost around £35million but Hernandez would be an easier deal to complete.
Hernández is unwanted at West Ham by new manager David Moyes.
Sanchez would likely set United back £25m should they convince Arsenal to sell this month, but the Gunners are likely to hold onto the Chilean until they sign a replacement.
Zlatan Ibrahimovic's latest injury woes have left United short of back-up and according to the Daily Telegraph, Old Trafford chiefs have made preliminary inquiries about a range of strikers, one of which is Arsenal man Alexis Sanchez.
Tony Khan, club's vice-chairman recently said: "As it's been the subject of a great deal of speculation, I'd like to announce that Ryan Sessegnon is staying with Fulham football club and will not be departing during this January transfer window". Jurgen Klopp wants £30 million for injury-prone striker Daniel Sturridge.