Shane Duffy celebrates one of his four Blackburn goals last season
The tabloid does however contradict itself somewhat, stating: "the offer has been turned down so far" - which suggests a previous bid was made.
Duffy helped Ireland to the last-16 of the European Championship
However, according to the Sun, Rovers plan to keep the Republic of Ireland international and offer him a new deal.
However, it stated that a delay in the deal has already caused Kenny Jackett's side to miss out on a number of targets, listing Nick Powell (Wigan Athletic), Ashley Fletcher (West Ham United) and Jake Bidwell (Queens Park Rangers) .
New QPR signing Jake Bidwell is one of three players said to have held unproductive talks with Wolves
Anderlecht striker Idrissa Sylla is another whose move is said to have collapsed, though the player has remained with his employers for the time being.