The Bhoys reportedly have until Tuesday to register one new signing in time for the Champions League.
Duffy is a reported Celtic target
The Bhoys were said to have stepped up their interest in the Republic of Ireland international, amid a shortage of senior centre-backs.
Brendan Rodgers' side were forced to field full-backs Mikael Lustig and Kieran Tierney alongside Erik Sviatchenko in a back three during Wednesday's Champions League victory against Lincoln Red Imps.
Lustig opened the scoring at Parkhead on Wednesday
The 3-0 win set up a third qualifying round date with FC Astana, and a trip to Kazakhstan has been scheduled for next week.
Despite the deadline for new signings to feature in that game passing on Thursday, Celtic have until the end of Tuesday to register one new face under the "wildcard" ruling, the National reports.
According to Coyle, though, the Bhoys will have to get a move on.
"In regards to Shane, there’s been no concrete offers from Celtic, in terms of a written offer, so that’s the only thing I can class as interest," the Rovers boss told the Lancashire Telegraph.
New Blackburn boss Coyle
"If there’s other people speculating, then I can’t really comment on that.
"I only deal in the facts and the fact is there’s been no concrete offer from Glasgow Celtic for Shane Duffy."
Celtic are likely to find Duffy difficult to prise away given a flurry of recent departures from Ewood Park.
The 24-year-old's defensive partner Grant Hanley completed a £6 million move to Newcastle United on Thursday, while Matthew Kilgallon and Tommy Spurr have left the club at the end of their contracts.
Hanley moved to Newcastle on Thursday