Boss Mourinho has remained close to Karanka, who was his assistant when he was in charge at Real Madrid, and is understood to have spoken to him about again becoming a member of his back-room team.
The Spaniard, who spent four years with Boro, got them promoted to the Premier League after seven seasons in the Championship before being sacked a fortnight ago with them struggling on their return to the top flight.
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Karanka’s last press conference for Boro after Man City loss
He has already been approached by clubs in his homeland, but it is understood none are of sufficient calibre to interest him.
Now, Mourinho has told him there is a place available in the dugout at Old Trafford, and Karanka seriously considering the option as he assesses his next move.
It is understood former Everton academy director Peter Vint may pitch up at Old Trafford, too.
If it happens, he may be following his highly-rated son Will, as the 15-year-old also appears to be heading to the Red Devils.
Vint has departed from Merseyside, just as the academy’s head of coaching Dave Adams shocked the club by leaving only ONE week into the job.