"I've told them I'd love to keep him and I'd love to buy him," City manager Keith Millen told BBC Radio Bristol.
"We'll discuss things, but they'll probably be thinking to get him some Premier League experience. If that happens there's nothing you can do."
The England Under-21 international spent last season on loan at Yeovil in League One and has made the step up to the Championship with ease.
Caulker joined the Robins in September shortly after making his sole Spurs appearance in their Carling Cup defeat by Arsenal.
He has started in 30 City matches, a third of which have resulted in clean sheets, and has also chipped in with two goals, one of which was a late header that salvaged a draw at table-topping QPR in front of Spurs manager Harry Redknapp.
BBC Radio Bristol commentator Ed Hadwin said: "He's the best young footballer I've watched live and has everything he needs to do well at a higher level.
"He's got pace, reads the game well and if he continues to progress he could well play for England in the future."
Source: BBC Sport
Source: BBC Sport