Ms Sturgeon recalled the conversation, which she joked made her sound “really up myself”, while appearing as a guest on Iain Dale’s All Talk show at the Edinburgh Fringe.
The broadcaster asked the First Minister whether she had ever met Ms Truss, who is the favourite to win the Conservative leadership contest.
Ms Sturgeon said the pair had spoken before a function at Glasgow’s Kelvingrove museum during the COP26 climate summit last year.
And she said the foreign secretary asked her how to get featured in Vogue.
Ms Sturgeon said: “We were there quite a bit early, so we were talking to each other.
"I remember this quite well actually. I had just done – and this is going to sound really up myself, it’s not meant to, OK – I’m telling this story as much against myself as it is against Liz Truss, in some respects.
"I’d just been interviewed by Vogue, so I’d just had a photo shoot in Vogue, as you do.
“And that was the main thing she wanted to talk to me about, she wanted to know how she could get into Vogue – and she calls me an attention-seeker.
"I said to her ‘they came and asked me’.
"I didn't really mean to do this, but I said to her it hadn't actually been my first time in Vogue, it had been my second time.
"It looked a little bit as if she'd swallowed a wasp.
"I'm sure she'll be in Vogue before too long."
Ms Sturgeon later added: "I remember it because there we were at the world's biggest climate change conference in Glasgow, world leaders about to arrive.
"That was the main topic of conversation she was interested in pursuing. And once we'd exhausted that, it kind of dried up.
"I'm sure we'll have many more conversations about many more substantive things."
Last week, Ms Truss during a Tory leadership hustings branded the First Minister an “attention-seeker” who is best ignored.
Ms Sturgeon told the Fringe audience she initially thought the comments were a spoof.
She said: “I am the democratically elected First Minister of Scotland, and when you say that I should be ignored, then effectively you’re saying that Scotland’s democratic choices and preferences should be ignored.
"And what you are effectively saying is that Scotland should be ignored.”