Brooks, 20, has impressed for the Blades this term but Bramall Lane chiefs expect to receive offers when the transfer window reopens.
The Daily Mirror claim Everton, Liverpool and Tottenham are all monitoring his form and lead the chase.
Brooks, who has two caps for Wales, is rated at £20million.
He is under contract until 2021 after signing a new four-year contract in October.
Blades boss Chris Wilder is desperate to hang on to Brooks but he is aware that club chiefs could sell if the price is right.
Wilder said: ”There’s a lot of off-the-record conversations, whether it be agents, or even clubs themselves asking what we are doing.
“But nothing changes from my point of view. David is not for sale because he is part and parcel of what we are doing going forward.
“Yes, I have had a conversation, and people understand he is an outstanding talent.
“But I have made it loud and clear that he isn’t for sale from my point of view. If anybody makes a bid, football now, it doesn’t really go through managers.
“It goes through chief executives and chairmen, that’s a decision the club have to make if they do get bids and offers from other clubs for our players.
“One thing I will say, I do look at our squad now and think we have a lot of assets in our football squad since we walked through the door.
“Even after 20 games in this division assets have gone up because they have been in the top six all season.
“Regarding David Brooks, or any other player, we have some really good players here and players who will be attractive propositions for other clubs.
“I would rather it be that way, than everybody think our players are garbage and not worth a dime.”