The Romanian, who partnered the Swede in Juventus's attack for the 2005-2006 season, is expected to join Ajaccio on a two-year deal next week.
Ibrahimovic now plays for last season's Ligue 1 runners-up, Paris Saint-Germain.
"I know well Zlatan, he is a good friend," the 33-year-old told French radio station RMC. "We will again be rivals, but from a distance.
"I take the challenge to see who scores more. Even if he is in a better team, it is not a problem for me. I would bet."
Mutu scored eight goals in 28 appearances for Cesena last season.