The 20-year-old has had a brilliant season and is expected to be part of the England squad that travels to Brazil for this summer's World Cup.
Reports have suggested Liverpool could offer £38million for Barkley, but, with tongue in cheek, Martinez said: "In terms of the speculation, we already turned down a £50million bid from (Manchester) United so we're not going to take £38million from Liverpool.
"It's quite enjoyable to speak about speculation, I think it shows how well our players are doing and those are the type of football compliments that we want coming our way."
Teenage defender John Stones has also been the subject of transfer speculation this week, and Martinez added: "It's a good sign. It's not bad for a young man that is just starting his career."
The Spaniard was speaking before travelling to Anfield, where he was due to speak at Tuesday's memorial service to mark the 25th anniversary of the Hillsborough tragedy.
The service was also being screened at Goodison Park, with the Everton squad among those paying their respects to the 96 Liverpool fans who died.
Martinez said: "It's a real honour from my point of view to be able to represent Everton Football Club on such a significant day. We've always been shoulder to shoulder with our neighbour and will always be there."
Fourth-placed Everton will bid for an eighth successive Barclays Premier League victory when they take on Crystal Palace at Goodison Park on Wednesday.