Vale are currently on the lookout for a new manager after former boss Rob Page left the job for Northampton Town.
The Staffordshire club's chairman, Norman Smurthwaite, confirmed that the United boss did call him with the recommendation and both parties are set to meet this week.
"Up until recently I thought it was a wind-up," Smurthwaite said.
"But the people who were supposed to be contacting me have done so."
Mourinho also had a hand in the Sheffield Wednesday appointment of fellow Portuguese Carlos Carvalhal last year and helped his former Real Madrid assistant Aitor Karanka land the Middlesbrough job in 2013.