The speculation follows Ferrari president Luca di Montezemolo ruling out Sergio Perez as Felipe Massa's 2013 successor, due to his lack of experience.
Finn Kovalainen, 30, is on the market after three years of rebuilding his reputation at Caterham, following his less-than-shining first three years in F1 at Renault and McLaren.
The Finnish broadcaster MTV3 said representatives of Kovalainen's management team at IMG Worldwide will travel to Maranello next week.
However, some consider Force India's Nico Hulkenberg as a more likely candidate to oust Brazilian Massa.
But, given Montezemolo's comments about experience, the 25-year-old German is only marginally more experienced than Mexican Perez.
A Ferrari spokesman told Brazil's O Estado de S.Paulo newspaper: "Do not apply what our president said (about experience) to other drivers.
"He (Montezemolo) was asked about Perez, and the response was specific to him."
The newspaper also said it doubts Ferrari's 2007 title winner Kimi Raikkonen is a candidate.
"Forget Ferrari. Kimi is not going there," a source close to the Lotus driver is quoted as saying.