However, Martinez has insisted that he has no plan of selling the Costa Rica international.
"I'm very surprised to hear that,” the Spaniard told Sky Sports. “You all know what we think of Bryan here.
”He's had a terrible season with injury but we fully expect him to be back and at full strength for us next season.”
Oviedo joined Everton from FC Copenhagen in the summer of 2012 when Moyes was in charge of the Toffees.
The versatile 25-year-old, who can play as a left-winger and as a left-back, has not made himself a first-team regular at Goodison Park, though, largely due to injuries.
The 25-year-old has played in six Premier League matches this season, creating three chances and having a pass accuracy of 76% in the process.
Last season, Oviedo scored two goals and created eight chances in nine league appearances, while in the 2012-13 campaign, he played 15 Premier League games.