Deulofeu spent last season on loan at Goodison Park and helped Martinez's side secure a fifth-place Premier League finish and Europa League qualification.
The 20-year-old forward said: "I had one lovely year with him, which was a great experience. He helped me a lot.
"If one day he came to Barcelona, he would be more than welcome and it would be good for him."
Everton broke their transfer record this week by splashing out £28million on Chelsea's Belgium striker Romelu Lukaku, another player who excelled while on loan with the Toffees last term.
And Deulofeu has backed his former team-mate to continue shining for the Merseysiders.
"I think Lukaku is a really great footballer - he helped Everton last year very much indeed," Deulofeu added.
"He has huge quality and I think he will do very well at Everton this season. If Chelsea decided to sell Lukaku, it is because they have their reasons.
"The only thing I can say is that I wish the best for him - I am happy for him to go to Everton because he is going to have a great season, which will help him a lot."
Following his successful stint in English football, Deulofeu is hoping to break into the Barcelona first team during the forthcoming season.
Such an achievement would be no mean feat given the plethora of attacking options available at the Catalan club, but Deulofeu has immense confidence in his own ability.
"I don't think it is a particularly difficult season (to break through)," the Spain international said.
"I believe in myself. I am very enthusiastic and I am going to try as hard as I can to show everybody that I can play for the first team."