Rovers last week saw a second offer rejected for the 27-year-old, who has 12 months remaining on his contract at Glanford Park.
Scunthorpe boss Brian Laws said the previous bid was "way below" his valuation of the player and Doncaster counterpart Paul Dickov appeared to put any further move for the wide man on hold.
Speaking last week, he told reporters at the club's training ground on Rovers' return to pre-season training: "He's a busy player who makes things happen and he has a bit of steel about him as well.
"But we have a valuation of the player and we won't be held to ransom, so that's now on the backburner."
Yet Rovers have now gone back in with another improved bid for Duffy which has been accepted by the Iron.