McKay, 22, who has been capped once for Scotland, has a year left on his contract.
McKay is one of a number of established first team players at Ibrox who appear not to feature in the Portuguese coach’s long-term plans.
Midfielder Andy Halliday, who was left out of the 30-man squad for the club’s first European tie in six years, will have talks with Azerbaijani side FC Gabala ahead of a potential season-long loan.
Wingers Michael O’Halloran and Harry Forrester, forward Joe Dodoo, defender Rob Kiernan and midfielder Matt Crooks were all absent from the squad list submitted to UEFA yesterday and have also been training with the kids.
Caixinha has made eight signings this summer, seven of whom were named in the European squad. Tomorrow’s first leg against Progres Niederkorn, of Luxembourg, is already a sell-out.