That would be bad news for Caterham's existing race drivers Giedo van der Garde and Charles Pic, who in that scenario would be locked out of formula one for now.
For Dutchman Frijns, however, Caterham could be his F1 lifelife, after the highly-rated 23-year-old lost his reserve seat at Sauber last year amid the Swiss team's financial troubles.
The Dutch newspaper Dagblad de Limburger reports that Frijns has "almost certainly" secured the Caterham race seat for 2014.
The report cited sources "close to the team and the driver", confirming that the deal is "almost complete".
With his reserve role, Frijns will reportedly get 16 guaranteed days at the wheel of Caterham's 2014 car -- eight on Friday mornings and eight additional test days.
Dagblad de Limburger added that Frijns' debut will be at Jerez later this month, followed by more running in Bahrain ahead of the start of the 2014 season.
Frijns would not confirm the news.
"We are working on options for 2014, and of course formula one is a part of this," he is quoted by Speed Week.