The Pompey star is top of Koeman's January shopping list as the Dutchman looks set to miss out on Liverpool's Mohamed Sissoko.
The Reds midfielder is close to agreeing a move to Juventus and Koeman, who had targeted Sissoko, has begun his search for alternatives.
However, Portsmouth boss Harry Redknapp - who has turned down the vacant Newcastle manager's job - is unlikely to be willing to part company with his £7million summer signing.
Koeman, though, is hopeful he can prise the Ghanaian international away from Fratton Park.
"We seem to have missed out on Mohamed Sissoko but Muntari plays a similar role and he would be excellent," Koeman told The Sun