Symonds' appointment still needs to be finalised and is subject to approval from banking regulators, Bloomberg reported https://bloom.bg/2jSPkal.
In January, the company said Chairman Philip Hampton would step down after more than three and a half years in the role.
Citing people familiar with the talks, Bloomberg said the appointment could happen in the coming weeks.
GSK did not immediately respond to a request for comment on the report.
(Reporting by Philip George in Bengaluru; editing by David Evans)