The Portuguese's name has been increasingly linked by the media with the job amid the struggles of incumbent Louis van Gaal to win over the United faithful.
The speculation was sent spinning into overdrive when Moratti, sister of former Inter president Massimo, let slip to reporters after a meeting with Mourinho that the former Chelsea boss "is going to Manchester".
Mourinho was in Milan to watch Inter take on Sampdoria amid reports in Italy that he might be interested in a return to the club he steered to Champions League glory in 2010, a suggestion he was quick to deny.
After Mourinho had visited former employer Massimo Moratti and his family for lunch, Bedy, filmed in a video interview with Calcio Mercato, said: "It was pleasant. He's still fantastic. He's been missed on a human level.
"Now he's happy -- he's going to Manchester and he's well."
Bedy, whose family retain a major stake in Inter, was a board member at the San Siro outfit and is honorary president of supporters' group Inter Club.
When Massimo was asked by reporters whether Mourinho was joining United, he was more circumspect, shrugging: "I'm not sure. I don't know if he wants to say".
Mourinho released a statement to La Stampa on Friday that denied he was interested in replacing Roberto Mancini as Inter coach.
"I have respect for every coach and every club. I'm not looking for a club, it is the clubs who seek me," he said.
"One thing I want to clarify, I will not be in charge next season. Inter have a project and that is (owner) Erick Thohir and Roberto Mancini."
(Reporting by Ian Chadband; Editing by Tony Jimenez)
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