"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,” she told LBC’s Iain Dale at the Edinburgh Fringe festival.
And Ms Truss might have turned a deeper shade of green, with envy, when Ms Sturgeon told her that it was not even her first time appearing in Vogue.
"It looked a little bit as if she'd swallowed a wasp,” Ms Sturgeon said, adding that she is sure the possible future PM will likely soon grace the hallowed pages.
Despite the event being hailed as a once in a generation chance to stop the climate crisis accelerating, Ms Sturgeon said being in Vogue was their main topic of conversation.
“I'm sure we'll have many more conversations about many more substantive things,” Ms Sturgeon said.
Ms Truss on Wednesday set out her stall to be the leader by taking questions from GB News viewers at an event in Leigh, Greater Manchester. She has not responded to Ms Sturgeon’s claims.
Earlier in the campaign Ms Truss reportedly called the Scottish leader an “attention seeker”.