The 20-year-old moved to Molineux on loan in the last campaign but was forced to return to his parent club last February after suffering a serious knee ligament injury.
Frimpong is still working his way back towards full fitness and has not been featuring recently for Arsenal's reserve team after suffering another injury.
The midfielder is keen on a loan move in order to get back to playing but, even with captain Karl Henry suspended, Solbakken, who only took over this summer, would just consider a January move.
"The situation is he wants to come to us," said Solbakken in the Express and Star. "But at the moment, he's coming back from the injury he got here.
"He has another small injury now and he hasn't played in Arsenal reserves' last two or three games.
"He has to get back to his best because he's only between 70 and 85 per cent fit which makes it hard for a midfielder such as David Davis, who's waiting for his chance.
"If we brought in Frimpong now and he isn't 100 per cent, what does it say about Davis?"
Solbakken added: "Frimpong can be a possibility for us in January when things might look differently.
"He'll be 100 per cent fit then if he doesn't get another injury."