The 63-year-old magazine editor has reportedly been planning top secret dinners to win over the 'Girls' creator - who plays hapless Hannah on the popular HBO series - and if successful, the curvy actress will appear on the cover of the US fashion bible.
A source told RadarOnline: ''Anna is trying to seduce Lena into bringing her next-generation audience into the Vogue brand, and she's willing to violate a lot of Vogue traditions to do it, including putting her on the cover even though she doesn't really conform to the body type that Vogue has featured for most of its history.''
The move would be a major cultural shift for the magazine which has done little to celebrate women of different sizes. So far, Adele is the only other famous plus-sized beauty in recent history to have landed a Vogue cover.
The source said: ''This dinner is a first step for Anna to see if Lena will play ball, but Anna's perspective is that they need each other.''
What's new in the music world this week?
'Sounds of Silence' was released on this day (January 17th) in 1966.
Listen to Alex Bayly performing 'Animal'.
Two weeks ahead of Independent Venue Week, Dry Cleaning made 'Britain's Best Small Venue 2015' (NME) the second port of call on their 2020 tour.
'Leave Home' was released on this day (January 10th) in 1977.
For their last gig of the year, The Libertines came back to their adopted hometown of Margate to finish off their latest tour.
Celebrating the birthday of David Bowie with his most legendary songs.