The club have refused to reveal any more details of the bids, or the clubs they are from, but at least one is likely to be for top scorer Billy Sharp.
The former Sheffield United youngster netted again in Saturday's 3-2 win over Bournemouth to underline his importance to the side, but this success has inevitably brought him a host of admirers higher up the Football League.
United are under no obligation to sell, but their resolve is likely to be tested to its limits from Monday - with January the only month when permanent moves for players can be completed.
There are no shortage of clubs lining up to bid for the talented youngster, with Premiership sides Watford and Manchester City both believed to be lining up bids.
And in the Championship, Wolves boss Mick McCarthy has spoken of his desire to sign Sharp along with his strike partner Andy Keogh.
As well as Sharp and Keogh, there are likely to be clubs considering moves for goalkeeper Joe Murphy, left-back Marcus Williams and midfielder Matty Sparrow.
But United's financial footing is secure, and with the club topping League One going into the New Year know an historic season could await if the current crop of players is kept together.