The 570,000 sq ft office scheme, comprising One and Two Southbank Place, is fully let to WeWork and Shell.
It is understood that Blackstone is not in exclusive talks for the asset, but that it is looknig to pay around £850m for the assets, which would reflect a yield of 4%.
WeWork pre-let its 280,000 headquarters at Two Southbank Place in June 2017, after Shell had committed to 250,000 sq ft in One Southbank Place.
Cushman & Wakefield was instructed to sell the buildings in May last year.
Last year it was reported that Singaporean investor Bright Ruby was in talks to buy the development for around £850m but that the deal fell out of bed at the end of September.
Source: Office - propertyweek.com