The 20-year-old England midfielder has been linked with a number of Premier League clubs after making a big impression with the Toffees this season.
Liverpool manager Brendan Rodgers is reportedly a big admirer of Barkley, but any bid is likely to be unsuccessful as Everton are keen to retain their young star.
When questioned about Barkley's future, Martinez said: "Well according to speculation, we turned down £50m from Man Utd so we certainly wouldn't accept £38m from Liverpool.
Barkley is not the only Everton player to be linked with a move as several major clubs monitor the progress of 19-year-old defender John Stones, but Martinez added: "I've not heard that but I'm not surprised and it's a compliment to him and Everton.
"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."
Martinez, who also dismissed suggestions he is interested in Espanyol striker Sergio Garcia, was speaking ahead of Wednesday's Premier League game against Crystal Palace.
The Toffees host the Eagles at Goodison Park as they bid to cement fourth place in the table, but Martinez is expecting no favours from Tony Pulis' men.
The Spaniard said: "We know how difficult it's going to be. The mind is very much set on the two big challenges that we have - two away games and three massive home games.
"Those home games start on Wednesday against Crystal Palace. You look at Palace and in my eyes they are the best defensive set-up in this league, especially when Tony Pulis arrived at the club.
"They don't concede many goals, if any, and they are on their best run of the year with three consecutive wins. So we're well aware at Everton that we need to create a special atmosphere under the floodlights and help the players face a very difficult fixture."