The Royals rejected a Wolves offer, believed to be in the region of £3million, for the stopper earlier in the week and McDermott is keen to keep him as part of his squad for an assault on the Championship title.
"We've had an offer from Wolves for Matt Mills which we turned down," McDermott said.
"It was way off our valuation and that was that. I don't know if they will come back for more - they may do - but I don't want to encourage clubs to bid for our players either.
"That's not part of my agenda. I want to keep our squad together, and add to it if possible."