However, Martinez has rubbished the reports by insisting that Everton are eager for the 25-year-old to commit his future to the Merseyside outfit.
"It must be a different Seamus Coleman because there has been absolutely no contact," Martinez said in Thursday's press conference.
The Spaniard added: "Seamus is having a great season and hopefully he can continue those levels. We want him here for many years to come."
The Republic of Ireland international joined Everton in 2009 from Sligo Rovers.