Millers chairman Denis Coleman told the 'Tiser that 5 championship clubs and 2 from league one had shown intrest, with Barnsley and Gypo Rovers tabling bids, both of which were rejected.
However, given the clubs financial plight any decent sized bid may well be accepted.
Speaking to the advertiser, Coleman said: "We will do everything in our power to keep Lee Williamson and ideally I would like to offer him a 1 year extension to the 12 months remaining on his current contract."
"Seven clubs, including Barnsley and Doncaster Rovers, have made some sort of enquiry. I can assure supporters that Lee Williamson won't go for a penny less than we think he is worth in the current transfer market and ideaally to a club at a higher level where he can further his career. He deserves that."
"My concern is that the lad could become unsettled. We pride ourselves on looking after the welfare of our players and we want to do the best for Lee. As things stand he remains a key part of our plans for the new season."
Williamson is expected to make an appearance during tomorrrows game against Gretna which kicks off at 3pm.