The Scottish champions found themselves in a transfer saga in January when they made a move for the Motherwell star.
After a fee had been agreed between the two clubs in June, Turnbull rejected the terms of the contract which saw Celtic issue a statement via Twitter.
It read: "Celtic was pleased to agree a record-breaking fee with Motherwell FC and we have quickly followed this up with a fantastic offer to the player through his agent.
"Celtic is content that it has made a magnificent offer and it is now up to the agent and player to decide if the player wants to join Celtic. If not, we move on."
It appeared the deal was dead before it was resurrected with a £3.25million transfer in the offing.
Then the medical revealed the player required "immediate preventative" surgery on his knee.
With the player due back in January, Celtic may return with a new offer, via Daily Record.
It may be the first bit of business done by transfer chief Nick Hammond, who is due to be appointed head of recruitment on a full-time basis.
The former Reading director of football worked for the club in the summer following the departure of Lee Congerton to Leicester City.
The Scottish Sun report he will sign a long-term contract with Celtic.