Drinkwater spent his youth career with United without making a senior appearance at Old Trafford, but it has now been suggested that the North-West giants are keen to tempt the England international back to the club.
Ranieri has confirmed that the player will remain at the King Power Stadium, but he feels that speculation linking members of his first-team squad with lucrative moves elsewhere should be taken as a positive.
The Italian told reporters: "It's speculation. I'm surprised, because it's usually a month before the window opens that this sort of speculation starts.
"But now, is good. When big teams want our players, it is good for us. One year ago, no-one was asking about our players. Now there are big big teams asking.
"Now they must be proud, but continue in this way. [Drinkwater] has signed a new contract, he doesn't have a [release] clause. If he wants to go to Man U, OK, but we want to keep him."
Ranieri takes his side to face United at Old Trafford on Saturday.