Neither striker has made a huge impression since joining the Scottish Premiership side.
Former Celtic striker Charlie Nicholas has claimed that he has had enough of Carlton Cole and Colin Kazim-Richards and believes that the Hoops need to concentrate their efforts on developing their own crop of forwards, the Evening Times reports.
Both strikers moved to Parkhead during this past season, but neither has really given the slightest hint that they would be capable of challenging for Leigh Griffiths' spot in the first-team, having managed just one goal and one assist - both of which have come from Kazim-Richards - in the Scottish Premiership.
And Nicholas believes that it is already time to give up on the hapless pair and turn their attention to giving some of the academy prospects a chance.
"I've had enough of Cole and Kazim-Richards - they don't bring anything to the party, they don't add anything to the fabric of this club," he told the Evening Times.
"I want to see the younger strikers developed and if they're not good enough then they're not good enough."
While very few will be expecting Jack Aitchison to be receiving the same number of opportunities next season that Kieran Tierney has been given this past campaign, the 16-year-old proved that he has some potential during his debut by scoring with his first touch during their final day win over Motherwell.
And with the youngster surely earning considerably smaller wages than Cole and Kazim-Richards, Nicholas' desire to see the club concentrate on their youth ranks rather than bring in back-up options may actually be in the Hoops' best interests as it may free up funds and provide their prospects with first-team opportunities.