Real Madrid’s former Tottenham midfielder was on the new Manchester United manager’s original list of targets – before Moyes made Cesc Fabregas his top priority.
But with Barcelona insisting that Fabregas is not for sale £30million-rated Modric is back on Moyes’ radar.
Champions United haven’t given up on Fabregas yet but it would now take a remarkable U-turn by Barca for the deal to go through.
Modric 27 has not established himself as a regular starter at Real.
Another option for Moyes - though a different style of player - is his former Everton midfielder Marouane Fellaini.
Nemanja Vidic meanwhile is training well after a sciatica problem kept him out United’s pre-season tour of the Far East and Australia.
United’s club captain is now set to make the friendly in Sweden against AIK Stockholm on Tuesday week.