Hamilton switching to Mercedes would theoretically open the McLaren seat to Kovalainen, but still the Finn has advised his former teammate to stay put.
"If I was him, I would stay there," the 30-year-old told the Daily Mail.
"McLaren is a great, great team and every year they are there or thereabouts and if they have some difficulties they are able to come back."
Kovalainen questioned whether McLaren-to-Mercedes is the wisest choice for Hamilton.
"There are not a lot of better places than McLaren in terms of history, facilities, stability and budget," he insisted.
"But in the end it is Lewis' decision and sometimes you might feel like you need a change."
Kovalainen, who has also been linked with Sauber and Lotus, said he is yet to speak with Caterham officials about the future beyond his 2012 contract.
"I've been there since the beginning so it's a big deal for me but of course I want to move forward and to move higher up the grid," he admitted.
"I will talk to them (Caterham) first and then after that I will see where I am, what I need to do, and make the next plan from there."