The Portuguese coach is said to have told the Dutch midfielder that moving to England was not the right option this summer despite interest from Sir Alex Ferguson's outfit
The 27-year-old Netherlands international has admitted that he spoke with the Premier League side over a move to Old Trafford after the Italians considered selling him.
However, the transfer was never forthcoming and Sneijder admits Mourinho influenced his decision.
"Mourinho called me and he told me to stay. He has an Inter heart and he has always told me to remain," Sneijder told La Gazzetta dello Sport.
"I am happy to have stayed because I never wanted to leave and so I no longer want to speak about Manchester United."
Outlining how the talks evolved, Sneijder said: "My agent called me and told me Inter wanted to sell. I spoke with Manchester United, but then the Eto'o sale started and so things changed."
Goal.com reported earlier in the summer that Inter had reached an agreement with Manchester United over a fee for the Dutchman, but his wage demands proved problematic in discussions, even though the playmaker wanted to move to Old Trafford after expressing no interest in a move to Manchester City.
Agent Kia Joorabchian has claimed that City attempted to offer Carlos Tevez to Inter in exchange for Sneijder.
"Manchester City? I don't know anything about this. I am happy at Inter," he said.
"I have a contract until 2015 and I want to respect it."
Inter play Palermo next Sunday and Sneijder is likely to feature for the Netherlands against Finland in Tuesday's Euro 2012 qualifier.