But he has been snapped up by Caterham for 2014, with team owner Tony Fernandes admitting 22-year-old rookie Frijns was even considered for a race seat.
"Robin has the pure speed," Caterham team boss Cyril Abiteboul is quoted by the Dutch newspaper De Telegraaf. "He has already made a big impression on our engineers during his hours in the simulator.
"Robin definitely has the talent to advance to the top of our sport."
Team supremo Fernandes, meanwhile, called Frijns - the 2012 Formula Renault 3.5 champion - "the most exciting young driver out there at the moment".
He said the Dutchman was considered for a race seat in 2014 "but in the end we decided to be cautious".