Preston have criticised Championship rivals Nottingham Forest for their public pursuit of Deepdale skipper Paul McKenna.
Forest boss Billy Davies, who worked with the long-serving McKenna during his time at the North End helm, revealed the latest offer was in the region of £750,000.
The City Ground club's latest approach was the third to be rejected by Preston and chairman Derek Shaw is becoming frustrated by the situation.
He told Preston's official website: "I can confirm last week we did receive a third bid from Nottingham Forest for Paul McKenna, but we again turned it down.
"We do not like to do our business in the public arena and would not have publicised this had comments not been made about it in Nottingham.
"We do not believe it is in anybody's interests to discuss transfer information unless something changes and these bids have clearly been unacceptable to us."