Caulker, who has one cap and one goal for England, was in fine form last season but couldn’t do it all on his own as Cardiff were relegated to the Championship.
QPR replaced the Welsh club in the Premier League and are looking to make Caulker their first major signing of the summer, with a fee of around £8million being agreed.
The 22-year-old will now be left to make his own decision, but Solskjaer confirms QPR are the only team in for his captain.
“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.
Crystal Palace were expected to make a move for Caulker but the bad blood between Palace and Cardiff has prevented that deal materialising.