The Toffees are enjoying their best Premier League season to date at this stage, having taken a record 60 points from 31 matches to surpass the 57 they had from 31 in 2007-08 and put them within touching distance of the top four.
Victory over fourth-placed Arsenal at home on Sunday would take them to within a point of the Gunners with a match in hand and raise the prospect of only their second qualification for Europe's premier club competition.
Lukaku's agent claimed this week he had been speaking to Tottenham about the Belgium international, who is on loan from Chelsea, but suggested the prospect of Champions League football with Everton meant the Merseysiders still held the upper hand.
Martinez, however, believes Sunday's game - and indeed the rest of the season - is not pivotal to their progress as a club.
"It is not about getting to the Champions League or not, it is more about the focus of the club and we want to carry on growing," he said.
"A lot has been said about that (Champions League determining Lukaku's future) but I don't think it is that straightforward.
"We want to be a football club who get into the Champions League consistently and that is important for a young footballer who wants to fulfil his potential.
"I truly believe Romelu has so far found that experience very much what he needed from a personal point of view.
"There is going to be a lot of speculation as Romelu has been performing extremely well.
"He is fulfilling his potential, which I believe is huge, and all we want is for him to concentrate on the next seven games.
"At the moment it has no effect on us at all."
Sunday's fixture is being billed as a Champions League qualification decider but Martinez rejects that notion.
He feels even if one team loses at the weekend they will not be completely ruled out of the race - especially if it is his side with their match in hand.
"What we have achieved is the opportunity to fight for a top-four finish and that is a remarkable achievement," he added.
"The statistics very much reflect every year it is harder to break into the top four; in the history of the Premier League if you had 60 points or more after 31 games you were always guaranteed to finish top-four.
"Now you have five teams who have done that so one of those teams will finish outside the top four.
"Arsenal at the weekend is a great opportunity but winning that game does not guarantee you finishing in the top four while losing it does not mean you are out of the race.
"We are fighting with a direct rival who have been in this situation every single season and they one of the best in European football in terms of getting consecutively into the Champions League.
"They are used to the pressure. They have always found a way to cope with expectations over the season so I don't think it will have a bearing on the game.
"They have full internationals who know how to handle it."
Victory for Everton would be a significant boost for them, having drawn at the Emirates Stadium in the league before losing an FA Cup quarter-final 4-1 there last month.
"The quarter-final left us with a sour taste and we need to make sure we use Sunday's game and the effect of Goodison to perform as well as we can," said Martinez, whose side are on a five-match unbeaten run.
"It could have a huge bearing because internally there is nothing better than carrying on a winning streak as that would allow you to go into the next 18 points with incredible momentum."