An auction of the two brands was supposed to start later this month with Irn-Bru maker AG Barr touted as one likely bidder alongside a number of private equity companies including CVC, Lion Capital and Blackstone.
AG Barr chief executive Roger White said in July the company would always be interested in brands it could add value to.
However Suntory has now emerged as the front-runner for Ribena and Lucozade and hopes to clinch the acquisition before an auction process formally kicks-off.
GSK announced in April it was looking to offload the two brands, which have combined annual sales of more than £500 million.
Lucozade, launched in 1927, and Ribena, introduced in 1937, have the bulk of their sales in Britain but GSK is reshaping its consumer health operations to focus on emerging markets. JP Morgan and Greenhill are acting for GSK, on the disposal.
Suntory, perhaps best known for its whisky, has previously indicated it is keen to expand its European arm which already owns Orangina Schweppes and has bases in France and the Netherlands.
GSK and Suntory declined to comment.