The 23-year-old has also been linked with United’s rivals Liverpool in recent weeks.
Gaitan’s current contract with Benfica is set to expire in the summer of 2016.
United boss Sir Alex Ferguson was reportedly impressed by the winger’s performance against his side in September in the Champions League.
He said: “I am very lucky to play for a club like Benfica.
“I have been flattered by the rumours from the Premier League, but my desire is to remain with Benfica until the end of my deal.
“It’s nice that Ferguson has spoken very well of me. But Manchester United is only in my head because it will be our next match in the Champions League.
“It’s a big match and I want to go and obtain our pass for the second round.”
