Doncaster have made forward Dany N'Guessan their sixth summer signing.
Tottenham have confirmed that Romanian defender Vlad Chiriches has completed a move to Napoli.
Solskjaer confirmed the clubs have reached an agreement and admits it is down to the centre-back as to whether he will leave the Cardiff City Stadium.
Although a deal appears to be close with Harry Redknapp’s QPR, who replaced Cardiff in the Premier League after winning the Championship playoff, Liverpool and Southampton are also reported to be interested in the 22-year-old.
Caulker joined Cardiff last summer from Tottenham but was unable to keep the club in the Premier League, although he did impress personally, featuring in every minute of the Bluebirds’ campaign and netting crucial goals.
The one-cap England international now looks set to return to the Premier League and, despite admitting it will be a loss for Cardiff, Solskjaer is keen to see a deal completed quickly.
“The clubs have agreed a fee,” the Cardiff boss told Wales Online. “It’s been accepted and now it is up to Steven to decide. At the moment QPR is the only one I know about. I have spoken to them.
“It’s up to Steven if he goes. Of course the lure of the Premier League might be too much for us to hope he might stay here. He has to make that decision.
“You want to get the business done as soon as possible. We’ve shown that ourselves by signing players early on in the summer. It makes it easier then to get a settled squad.”