The 32-year-old remains with the Parkhead outfit but no decision has yet been made.
It's probably about time, though, that they actually made one.
Indeed, the longer the uncertainty lingers, the less helpful it will be for Celtic. Fans want a new striker and players want to know if there is a new team-mate coming in.
That's why - whether it's yes or no - a decision is better coming sooner rather than later.
For, really, what more do Deila and co need to know about Cole? The former West Ham United forward is a hard worker who does what he says on the tin. All that needs to be assessed is whether he's fit enough and the Bhoys setup would surely have ascertained that by now.
RD on Carlton Cole: "He's still here but not been doing training with the ball so we haven't assessed anything further with him." (MH)— Celtic Football Club (@celticfc) October 15, 2015
With the 32-year-old a free agent, the risk factor is minimal. Cole should ideally be signed until the end of the season to help Celtic out, with things reviewed at the conclusion of the campaign.
But, even if Deila isn't keen on the striker, Celtic are better off putting him and those hoping for a move out of their misery.
It isn't the biggest issue in the world for the Bhoys right now - but the decision-making process should be a little speedier.