The Herald Scotland reports that Blackett is set to join Celtic on a season-long loan.
Reports claim the deal will include a clause to buy fee of £4million should both clubs agree at the end of the season.
Everton have also been strongly linked with the youngster, who signed a contract extension at Old Trafford in February.
The 21-year-old made 12 first team appearances for United last season, but has yet to feature for in Louis van Gaal’s side this season.
