Turnbull has made eight league starts this season and has been firmly in and out of the Celtic starting eleven under Brendan Rodgers.
However, he has still managed to score seven times in the Scottish Premiership and has a happy knack of scoring goals from midfield.
Hartson conceded that players of his ability are worth their weight in gold because of their ability to find the back of the net regularly despite being a midfield player.
However, the former Celtic star admitted that his future at the club does not look promising as it seems Brendan Rodgers prefers other midfielders over him.
He insisted that Celtic will try to find a way to cash in on Turnbull when the transfer window opens in January.
Hartson said on the Go Radio Football Show: “Sometimes the writing is on the wall.
“I like David Turnbull and midfield players who can come back with double figures are worth their weight in gold.
“For me, he does that, but whether or not Brendan has got different ideas in terms of bringing another midfield player or the players he has got at the football club with [Reo] Hatate to come back.
“I like the lad but it looks like the writing is on the wall.
“I don’t believe Celtic will offer him a new contract or if they had, he turned it down, I don’t know.
“He is in and out, isn’t he?
“He is not [Callum] McGregor or [Matt] O’Riley, he is in and out of the team. He is out for the weekend and then he comes back in.
“My immediate thoughts are that he is one of the players they will look to sell.”
Turnbull’s contract will expire at the end of the season and January could be the last opportunity for Celtic to get some money in from his departure.