Republic of Ireland international Coleman has impressed many with his barnstorming displays from right-back this season, chipping in with a number of crucial goals.
The latest of those came in dramatic fashion on Saturday as his last-minute winner saw Everton to a 2-1 win over Cardiff City at Goodison Park to keep them firmly in the hunt for European football next season.
There had been speculation that former Everton boss David Moyes would bring Coleman to Old Trafford in the close-season, but Martinez brushed aside any reports of contact between the two clubs.
"It must be a different Seamus Coleman because we've never had any talks with anyone," he said.
"Seamus has had a very good season, we want that to continue and in the next 10 games we want him to carry on with the same levels.
"He's a very, very important player at Everton and we want him to stay here for a long, long time."
Coleman has scored a total of six goals in 26 Premier League outings this season, and has racked up 133 appearances in all competitions since arriving on Merseyside from Sligo Rovers for a reported £60,000 in January 2009.
