GlaxoSmithKline (GSK), Britain’s biggest drugs company, is in advanced talks to recruit Sir Philip Hampton as its next chairman, an appointment that will coincide with his exit from the state-backed Royal Bank of Scotland (RBS).

Sky News has learnt that Sir Philip’s appointment could be announced by GSK as soon as next month.

If confirmed, he would be joining the pharmaceuticals giant during a period in which it is embroiled in a wide-ranging bribery scandal in China and possibly other markets.

A person close to the talks said negotiations with Sir Philip were “close to being a done deal”.

He is likely to join GSK as a non-executive director or deputy chairman ahead of moving into the chairman’s seat later in 2015.

The precise timing of a formal announcement and Sir Philip’s arrival have yet to be determined, and either side could still back away from the appointment, the source added.

GSK’s next chairman will replace Sir Christopher Gent, who has been in place for almost a decade.

At the drugs company’s annual meeting earlier this year, Sir Christopher said it hoped to announce news of his successor during 2014.

“I…expect to stand down at the end of 2015 having succeeded in finding a candidate who of course you will have the opportunity to elect and re-elect in due course,” he told GSK’s shareholders.

The situation is complicated by RBS’s need to recruit a new chairman, who is likely to want to know which party will form a government after next May’s general election.

Parachuted in alongside Stephen Hester shortly after the bank’s £45.5bn taxpayer rescue in early 2009, Sir Philip will mark his sixth anniversary at RBS next February.

He has said repeatedly that company chairmen should look to serve for between five and seven years, although friends say he will not leave RBS until his successor is in place.

Sky News revealed earlier this year that RBS had begun planning for Sir Philip’s departure, but recruiting a heavyweight replacement will be a difficult assignment.

The Government remains years away from a full privatisation of its majority stake in the bank, while RBS faces uncertainty from a UK competition inquiry and regulatory probes covering alleged manipulation in foreign exchange and other markets.

Nonetheless, Sir Philip’s in-tray at GSK could prove to be only slightly less challenging than the one with which he has dealt at RBS.

Sir Andrew Witty, the pharmaceutical group’s chief executive, was forced to warn on profits last month as the company introduces products which could help offset a decline in sales of Advair, its best-selling asthma medicine.

On Friday, the trial is expected to start in Shanghai of a British businessman and his wife on charges of illegally obtaining private information during the course of work they were carrying out for GSK.

A sex tape involving Mark Reilly, the head of GSK’s operations in China, was sent to Sir Andrew and other executives shortly before Beijing launched a probe into the alleged bribery of doctors.

GSK and RBS declined to comment.