The highly rated Finn Kovalainen is on the market because Caterham is reportedly considering signing the pay-driver Giedo van der Garde.
However, MTV acknowledged that Frenchman Grosjean, despite Lotus' deliberations and the 26-year-old's numerous incidents in 2012, is "more likely" than Kovalainen to line up alongside Kimi Raikkonen next season.
But Germany's authoritative Auto Motor und Sport said there is truth behind reports Lotus is seriously considering ousting Grosjean.
"Many suspect that Gerard Lopez will persuade Grosjean's sponsor Total to spend more money," read the report by correspondents Tobias Grunen and Michael Schmidt.
"But even Total has a problem with this protege. The French oil company has a safety campaign for public roads, and the face of a 'crash driver' doesn't fit."