Speaking exclusively to Football Insider, the ex-Premier League and England defender insisted Celtic will not have a “huge” window because clubs will not be willing to lose key players in January.
As quoted by BBC Sport, Ange Postecoglou revealed he was “confident” he can bring in more players in January.
The Celtic boss insisted the board have been “supportive” during discussions about recruitment.
The club are still in the middle of a major rebuild after finishing 25 points behind Rangers last season.
And Mills has warned it will not be easy to complete major deals during the winter window.
He told Football Insider correspondent Connor Whitley: “It’s very, very difficult to pick up players in January.
“They’re not out of contract, they’re not picking up free transfers.
“Teams are more reluctant to let players go because it thins out their squad and they can’t bring in a replacement.
“The January transfer window is often a couple of loans here and there. It’s very, very difficult to do any serious business in January.
“Unless you’ve already done that business in August knowing full well they’re going to come in January.
“You also might have to get some players out too.
“I still think it will be a relatively quiet window in January, Celtic might get a couple of loan signings in. I don’t see any big signings coming in January.”