The move would show that Chinese companies remain keen to enter the supplement market, despite several high-profile takeovers in the last year.
Last year Swisse Wellness was bought by Hong Kong-listed Biostime International Holdings for $1.67bn.
In June, China's Xiwang Foodstuffs bought Iovate Health Sciences International in a deal worth about $730 million.
Then in August, Shanghai Pharmaceutical Holdings and China-based private-equity firm Primavera Capital Group bought Australian company Vitaco Holdings.
And in our Business Monitor round-up published earlier this week, we reported how Ausnutria had taken a 75 per cent stake in Australian outfit Nutrition Care Pharmaceuticals.
According to the Wall Street Journal, GNC has met with a number of potential buyers with a view to striking a deal that could be worth $4bn including debt.
It has been suggested that interested Chinese companies include Shanghai-based Fosun Group and investment firm ZZ Capital International.
GNC has declined to comment on the issue, and its shares surged by 10 per cent to $21.49 a share on the back of the reports.
In July GNC’s chief executive officer Michael Archbold resigned and stepped down from the board of directors amid falling sales. Former PetSmart CEO Robert Moran replaced him on an interim basis.
Sales in the first the quarter of this year, April-June, were $673.2m, down 2 per cent from $689.6m in the same quarter last year.
Archbold had been trying to turn around weak financial performance by cutting promotions and moving stores to a franchise model.
His dismissal came mid-way through a strategic review of the company, which many analysts predicted could lead to a sale.
Speaking at the time, GNC chairman Michael Hines said: “As we continue the strategic review process and move with urgency to improve performance, the board believes it is the right time to undertake this change to drive effective execution of our plans.”