The experienced centre-back made just two Premier League appearances last campaign under Maurizio Sarri.
"It's a shame he [Lampard] wasn't in last year when I was there," Cahill told talkSPORT.
"No, I'm only joking. It would have been very interesting to work under him, especially when you've played with him and know what he's like, it would have been an experience I would have relished.
"Leaving Chelsea was sad, but naturally everything has to come to an end."