The Championship side have already failed with two bids for the Rovers striker, who spent the final few months of last season on loan at Portman Road.
"We are in constructive dialogue with Blackburn Rovers," Sheepshanks told the East Anglian Daily Times.
"The ball is still in play and we have made a new proposal. There is a disagreement over values at the moment.
"I am hopeful a deal can be completed and we are determined to bring Franny to Ipswich if we can. But we cannot pay over the odds. Nor can we breach the pay structure at our club.