Cairney believes Chelsea will grant the Argentine to turn results around.
"I feel like they've got to give him more time because I feel like Graham Potter was fast," Cairney told the Footballer's Football Podcast.
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"There's a lot of players who have come through the door. They've spent a lot of money so you want results with that but it's not even been a season.
"I feel like he'll get more time. He's got a good reputation and he's managed top players in the past. I feel like he'll get more time but it's a tough one because people like that who spend that amount of money will run out of patience.