The Scottish Premiership side are reportedly yet to make any contact regarding the 24-year-old.
A report in the Evening Times has claimed that Celtic are expected to make their move for Blackburn Rovers defender Shane Duffy this week, but any potential deal will not involve James Forrest moving in the opposite direction.
The Evening Times reports that the Hoops are yet to make any contact regarding a move for the Republic of Ireland international - who will cost around £3.5m - but with Brendan Rodgers being a fan of the player, it now seems that they will step up their interest imminently.
However, while Rovers boss Owen Coyle is keen on Forrest, the Evening Times reports that the 25-year-old will not be heading to Ewood Park due to the number of wingers already in the squad.
While Rodgers may have been hoping to use Forrest as part of the deal - especially if he felt there was never going to be any progress regarding extending his current contract which expires in seven months (via Evening Times) - the short amount of time left on his deal may have meant that his inclusion in any transfer may not have actually lowered the overall price that significantly.
Celtic's James Forrest
But with the Bhoys arguably needing to add a new centre-back, Blackburn's apparent lack of interest in signing Forrest is unlikely to deter them from pursuing a deal.
Duffy was one of the most consistent performers in the Championship last season, so may be the perfect addition to bring some reliability to the Hoops' back-line.
And with the Evening Times reporting that the 24-year-old is entering the final year of his contract, Blackburn may decide that, if a suitable bid comes in, letting him go this summer makes more sense than letting him leave for nothing next year.
Celtic manager Brendan Rodgers