Mourinho has long retained an interest in the England international and tried to bring him to Chelsea during his time at Stamford Bridge.
Barkley has endured a mixed season for Everton and was criticised by manager Ronald Koeman at the start of the season.
Ross Barkley is wanted by Manchester United and Tottenham Everton ace Ross Barkley pictured for first time since bar attack Wed, April 12, 2017
Ross Barkley has been snapped arriving for training after he was attacked in a bar last weekend
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Ross Barkley hides from photographers as he arrives for training
And Cascarino has urged him to move abroad – but believes the 23-year-old will stay in England because of the dizzying wages on offer.
"I would love a young British player such as Ross Barkley to take a punt and join a European giant, like my old Ireland team-mate Liam Brady did when he left Arsenal for Juventus at the age of 24," Cascarino told The Times.
"Barkley would benefit as a person and a player from living in a different culture and playing a different brand of football. I’m slightly biased as I played abroad but I cannot recommend it highly enough.
Jose Mourinho wanted to sign Ross Barkley for Chelsea
"I look at Barkley’s situation with his contract at Everton and, even though I doubt he will, I think he should take a leaf out of Brady’s book. He will probably stay in England because of the wages he can command in the Premier League.
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"But look at how Gareth Bale has blossomed at Real Madrid. He was brilliant at Tottenham Hotspur but has gone up a level in Spain."
As well as the Red Devils, Tottenham have also been linked with a summer move.