The Hoops have been linked with Allen ever since Brendan Rodgers was appointed manager of the club last month.
Rodgers’ link to the Welshman is well-known, making him a pivotal part of a successful Swansea team before taking him to Liverpool in a £15m deal in 2012.
He even dubbed Allen the ‘Welsh Xavi’ at one point during their time together.
But Allen has found regular football at Liverpool hard to come by and could leave Anfield this summer – just one year before his contract expires.
Because of Rodgers, Celtic have been heavily linked and the Northern Irishman has even spoken about the possibility of signing Allen.
However it’s beginning to look increasingly unlikely following reports that Liverpool have knocked back an £8m bid from Swansea to sign the midfielder.
If that proves to be true then Celtic may need to spend more than £8m to tempt the Merseyside outfit into selling.
And if Allen keeps performing well for Wales at Euro 2016 then that prices could continue to increase.
Celtic’s transfer record is £6m – a fee they spent twice on signing Chris Sutton in 2000 and then John Hartson in 2001.
So going after Allen at that price would be a significant change in transfer policy considering club chief executive Peter Lawwell has shopped on a lower budget over recent years.
Hoops fans – would you spend £8m+ on signing Allen?