Dawson, 19, is in his first fullseason in the Football League having joined Dale from Radcliffe Borough last February.
In 12 months he has made a total of 28 appearances for Keith Hill's side, who are top of the League Two table, scoring nine goals.
Nigel Adkins, the Iron manager, confirmed to the Scunthorpe Telegraph that a bid had been made.
The Lancashire side are said to value the player higher than the bid, suggesting Scunthorpe are likely to have to up their offer if they are to secure Dawson.