Reports on Thursday morning claimed that United were making progress with a 15 million pounds deal for the Republic of Ireland full-back.
But Martinez insisted that there have been no such talks, and that he intends to hang on to Coleman, whose Goodison Park contract runs until 2017.
Asked about the reports that United were in negotiations to buy the 25-year-old, Martinez said: “It must be a different Seamus Coleman, because we’ve never had any conversations with anyone.
“The truth is that Seamus has been having a very good season and we want that to continue.
“He’s becoming a very important player at Everton. He’s going to be a very important player for his national team.
“And obviously we want Seamus to stay here for a long time, so it’s nothing to comment on.”
Coleman is one of four young Everton players — the others being James McCarthy, John Stones and Ross Barkley — set for contract extension talks at the end of the season.
And Martinez insisted that there was no need to bring forward those negotiations, despite United’s reported interest in Coleman, who moved to Goodison Park from Sligo Rovers for 60,000 pounds in 2008.
The manager said: “We’ve got a clear strategy as to how we want to keep this group of players together.
“We’ve got a new generation coming through, and we’re going to keep those players for as long as we can.”
Written by Steve Milne