The Spanish youngster, on a season-long loan from Barcelona, has made seven substitute appearances so far for the club, and has come on in their last three games.
Now Martinez says he is considering starting him in the clash with their local rivals after the international break.
"It has surprised me how quickly he has adapted to the British game, and to the demands of the Premier League," explained Martinez. "He is fighting hard for his place.
"I would have no concerns about putting him in against Liverpool, no.
"When you are able to play against Jan Vertonghen, and to cope with that, then it shows you he is ready for anything."
Despite talking of Deulofeu's possible inclusion in the derby, Martinez insists he cannot think about the match too much until the dozen players he has on international duty return.
"I can't really look forward (to the derby) yet, because we are losing 12 players with the Under-21s and the senior players," said Martinez.
"It is one of those situations where you keep your fingers crossed and hope that everything goes well.
"But you can imagine. All the fans have made it clear that they are excited about the derby. It's a special game, and I can't wait to feel Goodison Park at its best."
The Everton boss, though, is looking forward to his first taste of the derby clash.
"I have said before that it has felt very natural from day one. I need to thank everyone who works at the club, and the fans, who have made it so easy for me to be part of the football club," he said.
"Once you find out about the history of this club, it is very easy to feel part of it. It's special.
"Now I want it to carry on, and for us to keep winning games and make sure we can achieve something special."