The former Celtic striker believes that manager Neil Lennon must already have doubts over the 21-year-old striker.
Sutton made the comments in the wake of Celtic boss Lennon not including the Poland Under-21 international in his squad for the Scottish Premiership game against Heart of Midlothian on Wednesday evening.
Sutton said about Klimala on BT Sport, as transcribed by The Scottish Sun: ”Of course we don't know if he is injured but I suspect the truth is, we all watched him at the weekend, and there must be doubts.
"You spend £3.5million, and he hasn't had a run of games so he will need that, but we haven't seen anything just yet, any real positive attributes if I'm honest. He needs a run of games."
Klimala joined Celtic from Jagiellonia Białystok in the January transfer window for a fee reported by The Scottish Sun to be worth £3.5 million.
The youngster made 12 starts and five substitute appearances in the Ekstraklasa for Jagiellonia Białystok before his switch to Celtic last month, scoring seven goals in the process, according to WhoScored.
Celtic are 10 points clear at the top of the Scottish Premiership table at the moment, although second-placed and bitter Old Firm rivals Rangers have a game in hand.
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