Doumbia rediscovered some better form for Wolves at Middlesbrough on Saturday after recently returning to France to recharge his batteries, but Solbakken is expecting to be without him for an extended spell when the African Nations Cup gets underway next month.
"It's still up in the air at the moment," Solbakken told the club's official website. "There are many things involved and it's a big decision for everyone. We don't really want him to go, but we'll see what happens.
"If he wants to go and he's picked, it's no problem - we must be without him. It's as simple as that. There are international rules for this.
"In a way, I can influence it a little bit, but I'm not going to twist his arm. This is his country."
Solbakken revealed Doumbia's short-term future could influence his decision on whether to pursue his interest in former loan midfielder Emmanuel Frimpong.
Arsenal midfielder Frimpong had an injury-curtailed spell with Wolves last winter and although he is currently on loan at Charlton is due to return to the Emirates in January.
Solbakken added: "I think we've been right so far on this one. We've monitored his situation with Charlton and seen the games.
"He's better now than when he first went there. When he first went, he struggled a bit with his fitness. You could see that with the amount of minutes he played. Now he's playing a little bit more but not 90 minutes."