The British team, which won back-to-back drivers' titles in 2010-11 with Mikhail Aleshin and Robert Wickens, has struggled all winter to find drivers with sufficient budget, and it missed all of this year's pre-season testing.
It has continued to chase opportunities to enable it to start the season at Monza this weekend, but Carlin told AUTOSPORT he has now switched his attention to rejoining the series as soon as possible after the opener.
"We'd like to be at the second race," he said. "As soon as we get an economic solution that's workable we'll be back out there.
"But until then, the cars will stay parked. We're not even close [in terms of funding]."
AUTOSPORT understands that series bosses are disappointed to have effectively lost one of FR3.5's most loyal teams, but Carlin added that Renault Sport has been very supportive of his team's situation.
"At the moment Renault Sport have been very, very helpful to us, and hopefully we can repay that help by returning as soon as possible," he said.
"Right now I'm not even near 50 per cent of a budget. It would be stupid [to start the season].
"We've got sensible budgets for the other things we're doing and it seems silly to be pulling resource from that to subsidise World Series.
"We want to carry on though. We're a top team, and if we can get back there with some frontrunning drivers we can continue that."
Carlin did not rule out the possibility of another team taking over his entry.
"If [Renault] find someone that wants to take over the entry then that's their prerogative," he said.
"At the minute we are pushing to carry on. That's our intention."
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