The move would mean the closure of its UK head office in Brentford, west London, with the loss of up to 500 jobs, while further job cuts could ensue as back-office functions are transferred to the US.
The company was formed by the merger of SmithKline, the American pharmaceuticals business, with Beecham, the English drugs and consumer products company, in 1989. The group numbers among its bestsellers Tagamet, the anti-ulcer preparation, while Famvir, its anti-herpes treatment, has made strong progress since it was launched two years ago.
It also has a variety of consumer products, including Macleans toothpaste, Ribena, Lucozade and Horlicks, which form the residue of the old Beecham business.
Jan Leschly, who took over as chief executive in 1994 from Robert Bauman, once Britain's highest-paid executive of an FT-SE 100 index stock, is understood to spend relatively little time in the UK.
A company spokesman officially denied suggestions of a move. "There are no such plans," he said. Mr Leschly, he added, spent his time in all the regions where SB has operations, in proportion to revenues, and that the total for the UK was at least "one to two weeks a month."
But there is no doubt that, since the merger - which was touted at the time as a marriage of equals - the American side has dominated the business. The company has already made major cuts in the UK, the largest being the closure of the St Helens factory on Merseyside in 1994, with the loss of 480 jobs.
Sources inside SB say Mr Leschly dislikes commuting to London and has always preferred the group's US industry headquarters in Chicago.
One well-placed source confirmed that SB had been making plans to move and reincorporate in the US, though no final decision had yet been reached.
There would be compelling reasons for such a move which would benefit the business. Cost savings, after any initial restructuring provisions, would be substantial, while there would also be tax benefits.
A move to the US would also affirm the profoundly American nature of the company, while positioning it better for the continuing consolidation in the international health-care industry.
In what may be a veiled warning in the latest annual report and accounts, the company highlights its concerns over the Greenbury Committee proposals on executive remuneration. Chairman Sir Peter Walters said: "Such changes should not be so restrictive that they impede major global companies based in the UK from competing for the best management talent. The company is continuing its discussions with the Stock Exchange to ensure that full consideration is given to the international context in which we operate."
Last year, out of sales of pounds 7bn, pounds 3.3bn were in the US while only pounds 560m were in the UK - although there were sales of pounds 1.7bn to continental Europe.
The company employs more than 50,000 staff worldwide, the majority of them US-based.
In April, the company simplified its share structure, which took the form of equity units made up of A shares and B shares. The separate classes were replaced with a single class of ordinary share, with a cash payment to equity unit holders of $295m.