Kovalainen, 31, played down the comments.
"I have always had a good relationship with him (Gascoyne)," he said, "and my relationship with him will continue even now.
"Mike is a seasoned professional and he and I have worked together for a long time," Kovalainen told the Finnish broadcaster MTV3.
"The fact is that my negotiations are not with him. I talk to Tony Fernandes and Cyril Abiteboul.
"At the moment, the negotiations are continuing and I am not thinking about anything other than formula one. First, let's finish playing the game until the end.
"Then, when we know the outcome, think about what to do next," added Kovalainen, who moved to Caterham (then Lotus) in 2010 after being dropped by McLaren.
Gascoyne this week confirmed Caterham is considering replacing Kovalainen with a sponsored driver.