The Belgium international has been in the headlines this week after his new agent, Mino Raiola, suggested his client could leave Merseyside.
In an interview with Belgian newspaper Sudpresse, Raiola was quoted as saying "had [we] met each other earlier, he wouldn't have played for Everton" before going on to claim the striker would eventually "play for one of world's best teams".
Lukaku signed a five-year deal with Everton last year after joining from Chelsea for a club-record fee, and Martinez believes the 21-year-old can reach his potential with the club.
"From my view, Romelu is one of the most exciting signings we've ever made and that shows the commitment and investment in the club – he's an incredible talent, he's 21 and has a long-term contract so for me there is no issue," said Martinez.
"He [Raiola] is an agent who's just had a short period of time with his new client, and for whatever reason has made those comments.
"I've spoken with Rom – as I do all the players in those situations – about him deciding to change his agent, and that's his decision and he has every right to do that.
"He's a very important player for us, and we showed an incredible respect and integrity when we signed him for him and his career, and he showed the same to us."
Lukaku was absent from the 1-0 win over Southampton on Saturday as he continues to nurse a hamstring problem he suffered against QPR prior to the international break, but Martinez is hopeful the forward will be available for the trip to Swansea City next weekend.
"Romelu couldn't recover in time [for Southampton], but he will be assessed on Monday or Tuesday for Swansea," the Spaniard added.
"He's not far away – it could be a bit too early for the Swansea game but I think he's got a chance."
