Reports in the Belgian media on Thursday revealed that Lukaku's agent has been in contact in with Tottenham, while the possibility of making a full-time switch to Goodison Park from parent club Chelsea remains a possibility.
The 20-year-old striker, on a season-long loan at Everton, has caught the eye on Merseyside with 12 goals in 26 Premier League appearances, yet despite that return his immediate future at Stamford Bridge remains unclear.
Martinez refused to be drawn on whether the club plan to try and sign the youngster on a long-term basis, but he did suggest that Lukaku's decision will not be based on whether Everton play in Europe's premier competition next season.
"You need to understand there is going to be a lot of speculation and a lot of talk," he said.
"Romelu has been performing extremely well, you're going to get that sort of speculation when a player has been on loan and there's a bit of uncertainty.
"As a young man, I think he's fulfilling his potential. All we want is for him to focus on the next seven games, then whatever happens in the summer it's going to be good, with the season he's had it can only be positive.
"I think the next seven games are going to be very important to see where the next chapter is for Romelu, but it's not about whether we get into the Champions League or not, it's more about the focus of the football club.
"We want to carry on growing. We want to be a club that looks to get into the Champions League consistently, that's very important for a player that wants to continue developing."
Martinez is preparing his side for a crucial showdown with Arsenal on Sunday, in a match that has significant bearing on who will claim in the final Champions League spot.
Arsene Wenger's men currently hold a four-point advantage, although Everton have a game in hand.
However, Martinez believes that the fixture will not be decisive in the race for fourth, no matter the outcome.
He added: "Arsenal at the weekend is a great opportunity, a great occasion but in the same manner winning that game doesn't guarantee you the top four, if you lose it you're not out of the race.
"It's 21 points to fight for and it's how many we can get out of those."
Martinez is confident that midfielder Ross Barkley will feature, despite coming off early in the 3-1 over Fulham last weekend, but captain Phil Jagielka is unlikely to return from a hamstring injury.
