Private equity firm Blackstone Group
Despite the talks, Blackstone's participation in the deal appeared unlikely to happen, said the source, who requested anonymity because of the sensitive nature of the talks.
The source declined to elaborate, and Blackstone and Bright had no comment on the matter.
News of Bright Food's bid for GNC first emerged earlier in the week, with sources saying talks were at an advanced stage and a deal could be announced within days.
Under the deal being discussed, Bright Food would purchase GNC for $2.5-3 billion, a source told Reuters on Monday.
The potential acquisition of Pittsburgh-based GNC, which is owned by Ares Management and the Ontario Teachers' Pension Plan Board, would follow a failed attempt by Bright Food to buy Britain's United Buscuits for about $3.2 billion.
Shanghai-based Bright Food, best known for its dairy products, also recently lost a bidding war for Australian sugar refiner CSR
China has been aggressively snapping up overseas assets in the resources sector to feed its fast-growing economy, but a purchase of GNC marks a less common instance of a major acquisition in the U.S. consumer space by a Chinese company.
(Reporting by Megan Davies, writing by Doug Young; Editing by Chris Lewis and Ken Wills)