Both the Financial Times and Reuters have reported that sources with knowledge of the discussions could see the two British drinks brands valued at more than £1bn.
GSK said is does not comment on market speculation.
The company announced a strategic review of the two drinks brands following a 1% revenue decline in 2012, before announcing in April that it would sell of the brands by the end of the year.
In July Irn-Bru owner AG Barr was reported to be considering a possible £1bn bid for Lucozade and Ribena following its withdrawal from its proposed merger with Britvic. At the time, AG Barr was expected to be in open talks with private equity firms over the opportunity.
GSK last month announced it is splitting the company into two separate business operations to pave the way for a selling off of the Lucozade and Ribena brands.
However, GSK has maintained that it will continue developing new products and investing in advertising and promotional spend into the brands while preparing for the sale.
Peter Harding will lead the siphoned off business for the two brands, with Carol Smith who has been newly appointed as the UK and Ireland marketing director for Lucozade and Ribena.
Carlton Lawson will lead the GSK Consumer Healthcare business, which spans oral health, wellness, nutrition and skin health.