Martinez: Lukaku likely to miss Everton opener
Lukaku joined Everton from Chelsea 10 days ago in a club-record deal worth £28 million after a successful loan spell on Merseyside last season.
The Belgium international scored 16 goals last term, helping Everton to a fifth-place finish in Martinez's maiden season in charge.
He then scored in Belgium's 2-1 last-16 win over the United States at the World Cup as Marc Wilmots' men reached the quarter-finals in Brazil.
And, ahead of Everton's opening-day trip to Premier League new boys Leicester City next Saturday, Martinez is wary of risking the 21-year-old former Anderlecht man.
"When you have players coming back from the World Cup you have to decide if you want the players straight away or do you give them a bit of time to refresh and be ready to play for 10 months?" Martinez said.
"It will only be [Belgium winger] Kevin Mirallas and Rom who might not start the season. For Romelu, it will depend on how he adapts to work from now until August 16.
"There is a degree of risk if you put them into a situation so early. They've been training really well and are accumulating a lot of work."
Aside from Lukaku, defender Muhamed Besic and midfielder Gareth Barry have been among those to arrive at Goodison Park in the close season.
Martinez is willing to dip into the transfer market again, but stressed that Everton's remaining business will depend on the fitness of Arouna Kone and Bryan Oviedo - both of whom are recovering from long-term injuries.
"Towards the end of last season I said we needed six more players, but it wasn't six new players, it was six players," Martinez added.
"We have added Barry, Lukaku and Besic and we also have [full-back] Tony Hibbert who re-signed.
"We still need one or two, depending on how quickly Arouna Kone and Bryan Oviedo recover from their injuries."