Chairman Philip Hampton is said to have told shareholders that the company's board will prioritise succession planning in the next couple of years, although Witty is not expected to go until next year at the earliest.
Hampton is in no rush and is keen to ensure a considered and orderly transition, Reuters cited unidentified sources as saying. Witty himself is said to be set to play a role in finding his successor.
There has been speculation about takeover interest in Glaxo and some shareholders have called on the company to consider breaking itself up.
Witty, who has faced criticism from some about Glaxo's relatively lacklustre share price, has insisted Glaxo is better off intact than splitting itself into its constituent parts, such as pharmaceuticals and consumer health.
He told a news conference earlier this month: “When you look at the uncertainty of the general global environment, I actually think having a more balanced set of businesses is exactly the right course for us.”
Shares in Glaxo rose 3p to 1413.5p in early London trading.