D'Arcy underwent surgery in June on the right ankle injury he sustained in Leinster's Heineken Cup final victory over Northampton and is still in rehabilitation.
The clock is ticking for the Lions centre with Ireland departing for New Zealand on August 30 and McNaughton admits his participation is in doubt.
"Gordon is tight to make the World Cup. He recovers quickly and is running while bearing his full weight, so is making progress," he said.
"With these type of injuries, a week can tell us a lot - players can progress a lot in that time as well."
The likelihood of Ulster flanker Stephen Ferris, who is struggling with a knee problem, being fit for the World Cup is also shrouded in uncertainty.
McNaughton hopes the duo will compete in the latter stages of Ireland's warm-up campaign, which opens against Scotland at Murrayfield on Saturday.
Both are important players when fit and McNaughton refused to rule out the possibility of taking them to New Zealand without having seen any match action over the coming month.
"Gordon and Stephen face a race against time but are making progress," he said.
"If there is a likelihood of guys not playing before the World Cup then it's those two.
"We're hopeful that they may be ready for game time, maybe in match three or four of the summer series. They are unlikely to play in the first two games.
"It's a preference that they have some game time before they go, but we'll never say never on anybody.
"A player could be just a week away from full fitness but it would be dangerous to play him in a game.
"We always have that option. It's our preference that everyone will get some game time."
Brian O'Driscoll is another player who is unlikely to figure in the opening fixtures of Ireland's five-match tune-up series, which comprises of meetings with Scotland, France home and away, Connacht and England.
"Brian has been doing 80% of the work over the last two weeks. I'm not too concerned about him," said McNaughton.
"He has a problem with his shoulder/neck and has been having some traction on it.
"He's doing everything except contact this week, but is unlikely to play in the first two games."
There was more encouraging news on hooker Jerry Flannery and full-backs Rob Kearney and Geordan Murphy, all three of whom are available to face Scotland following lengthy lay-offs.
"Flannery (calf), Kearney (knee) and Murphy (ankle) are ready to go. They were involved in contact last week and are ready for game time," said McNaughton.
"Flannery has been out for quite a while now (since January).
"He has been getting specialist rehab on a one-to-one basis during the summer, but over the last two weeks has kept up fully in training.
"We're pleased to see him take part in everything from contact to scrummaging.
"In general the injury situation has been getting better over the last couple of weeks, but we have five matches and need to give guys game time.
"We're hopeful that every player will partake in some games."
Shane Jennings resumes contact work this week as he continues his comeback from a broken arm.
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