Representatives from FR3.5 teams, RPM and Renault Sport met at RPM's Barcelona offices on Thursday to discuss developments.
"[A] meeting took place in Barcelona together with all the Formula Renault 3.5 series teams representatives, RPM and Renault Sport in order to study the conditions and the feasibility of the handover of the series to RPM from 2016," a Renault statement said.
"Practical propositions were provided and will need to be investigated before a decision can be made.
"All the parties have the same intention to reach a successful conclusion.
"At the same time, Renault Sport will continue to support Formula Renault 2.0 and the Renault Sport Trophy, and to work on a new World Series by Renault format."
Reigning FR3.5 champion and Toro Rosso Formula 1 racer Carlos Sainz Jr is among those hoping the series can maintain its appeal without Renault's support.
"I'm not sure what package they will have," said Sainz. "I hope it keeps going and keeps bringing up young talent.
"I just hope it has a positive effect on the championship because it's one I appreciate a lot.
"As a driver [before competing in FR3.5] obviously you never feel you're the main event - at World Series you could feel that, and you could feel a bit more pressure because of that.
"So it makes you a bit more ready as a driver. It's a nice category and I just have good memories from it.
"There were always good crowds, and we also went to Monaco which you don't get to go to with many other categories. I wish all the best to the people there."
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