Their top scorer last season is reported to be subject of a £150,000 bid from City. Adam Pearson denies this, but says the club are interested.
Bairns manager John Hughes said to BBC Scotland: "There has been plenty of talk about it but, until we get a bid which we feel is acceptable for Darryl, he won't be going anywhere.
"He has another year to go on his contract and we are trying to get him to sign another year.
"But if they did put a reasonable bid in, we would look at it."
Duffy is thought to be number one target after City missed out on two other forwards last week.
Mamady Sidibe says Hull City were one of the clubs he turned down after leaving Gillingham. He signed a two-year deal with Stoke on Wednesday. Meanwhile, Sam Parkin has moved from Swindon to Ipswich for an undisclosed fee, rumoured to be around £450,000.