The 24-year-old spent the second-half of last season on loan at Aston Villa.
After a shaky start at Villa Park, Johnstone impressed and managed eight clean sheets in 21 appearances.
He's highly rated, but with David de Gea firmly established as United's No.1 his first-team opportunities look severely limited.
The Red Devils also have Sergio Romero as back up and Joel Pereira on their books.
West Brom, Huddersfield, Leicester, Villa and Middlesbrough have all been sniffing around.
According to The Mirror, Crystal Palace also look set to enter the race for his signature.
It's suggested new Palace boss Frank de Boer wants competition for Wayne Hennessey and Julian Speroni between the sticks.
Meanwhile Steve Mandanda is expected to return to France.
Speaking last season, Villa boss Steve Bruce admitted he wanted to keep Johnstone at the club.
He said: He’s grown into the role. He’s now more comfortable in the role – and he’s got that from playing.
“If there’s an opportunity that we can get him to play more next season I would love to do it.
“I will be having that conversation with Mr Mourinho when the time is right. But I hope we can extend it.”
Johnstone is yet to make a first-team appearance for United.
