The Welshman has been linked with joining his former boss at the Scottish Premiership side.
Joe Allen's agent has claimed that Celtic could struggle to find the funds to bring the Liverpool midfielder to Parkhead when asked about whether the 26-year-old making a move to reunite with Brendan Rodgers could be on the cards, the Daily Record reports.
The Welshman was a key part of the new Hoops boss' plans while he was in charge at Anfield and at Swansea previously. And with Allen finding opportunities more difficult to come by under Jurgen Klopp, the Record reports that there has been speculation regarding a potential switch to the Bhoys this summer.
But the player's agent, Glenn Corcoran has seemingly dampened talk of a move by insisting that he had no word from Liverpool that they were looking to sell, while also suggesting that the Scottish Premiership side may be priced out of the market anyway.
"I haven't given any thought whatsoever to it with regards to Celtic or any club," he told the Record.
"If Liverpool were willing to sell – and that is a big 'if' because I've not had that conversation with the club – they would ask for too much money for him.
"I don't know if Celtic at this moment would be willing to spend that sort of money and the wages would also be a massive issue."
While Allen - who the Record claims earns £45,000 a week on Merseyside - would undoubtedly be able to do an excellent job in the Hoops' midfield if he was to sign, it could certainly be argued that signing a new midfielder should be fairly low down on Rodgers' list of priorities.
He currently has a considerable number of options to pick from. And with Corcoran suggesting that bringing Allen to Celtic Park would be very expensive, that money could surely be better spent in other areas of the squad that need attention as they look to build a side capable of making an impression in the Champions League.