Signed on a season-long deal from Tottenham in September, Caulker has played a big part in the revival that has seen City haul themselves off the foot of the Championship table and move clear of the relegation zone.
Millen is confident the Premier League club will honour the agreement and that the England Under-21 international will remain at Ashton Gate.
"I don't see how Celtic can possibly take Steven on loan if he is already on loan to us. I'm not sure where these stories have come from, but I can assure our supporters there is nothing in them," said Millen. "We have an arrangement with Tottenham, who have agreed to let us take Steven on a youth loan for the whole season.
"I speak to Tottenham on a regular basis and they are happy with the progress he is making with us. He is playing regular first-team football at a good level and is learning his trade.
"My contacts at Tottenham say they are happy with that and have given assurances they will not go back on the deal we have. The only thing that will prevent that is if Spurs need to recall them at any time to play in their first team."
Source: PA
Source: PA