Mourinho, sacked by Chelsea two months ago, has been increasingly linked to Louis Van Gaal's job at United as the Dutchman continues to struggle at Old Trafford.
Reports on Friday claimed Mourinho had a "pre-contract" agreement with United, who lost 2-1 to Danish side Midtjylland in the Europa League on Thursday.
On Saturday Calciomercato.com claimed Bedy Moratti, the sister of former Inter chief Massimo, had lunch with Mourinho and his brother in Milan.
Both Mourinho and former Inter and Brazil striker Ronaldo will be guests of the club later Saturday when Inter host Sampdoria at the San Siro.
Mourinho led Inter to an unprecedented treble of league, Cup and Champions League in 2010 and, asked if he was missed at the club, Ms Moratti replied: "We miss him as a person, but now he's happy, he's going to Manchester (United)."