The Millers turned down a £100,000 bid from table toppers Crawley for the 15 goal striker and moved to quash other clubs making any bids earlier this week.
Boss Scott said: “Just because we are a League Two side and signed him for nothing, people think they can take the mick.
"If people come back with serious offers then clearly as a club we have to look at it but Lewis is grounded and as I said to him in the summer, you need to come and play 40 or 50 games in a season and show everyone how good you are and score the goals that you can."
The two Sheffield clubs have also been linked with Grabban by the local and national media but Scott continued: “To keep Lewis is our most feasible option. We have a new stadium to go into and these are encouraging times for the club.
“I don't want to sell him and neither does the chairman. If it's a big offer then you have to listen, but the figures being talked about at the moment are vastly short of what would even be considered.
“If he's going to go in this transfer window then it's going to be because it's an unbelievable deal we couldn't turn down.”