Major shareholders are said to be increasing pressure on the drugmaker's board to cut Walmsley's compensation package to more reflect her experience, Sky News reported on Thursday.
GSK share was up 0.30% to change hands at 1,680 pence on Friday morning at 10:00am GMT, extending a 14% gain over the past three months.
The FTSE 350 Pharmaceuticals & Biotechnology Index has gained 14.21% over the past three months.
Walmsley is currently the CEO of GSK Consumer Healthcare and will take the helm of the pharmaceutical company on April. She joined the board at the start of the year. GSK is the largest company to appoint a female CEO, joining a group of just seven women running the U.K.'s largest companies.
The compensation committee is said to be planning to put forward a package that includes a fixed salary of just under £1 million. Walmsley has been on a salary of £850,000 since she was appointed CEO in the fall.
Witty's total compensation was £6.6 million in 2015. He had a fixed salary of £1.1 million in 2016.
Sources told Sky that Walmsley's bonuses and long-term share awards will be worth less than those of Witty.
Shareholders have allegedly told the company that Walmsley's pay package should be lessened to more reflect her experience.
According to BoardEx, a relationship mapping service from TheStreet (TST , Walmsley joined GSK in 2010, after 17 years at L'Oreal (LRLCY . She became CEO of the consumer healthcare division, whose brands include Sensodyne toothpaste, in January 2016.
Committee chair Urs Rohner, who is also the chairman of Credit Suisse, is said to be in consultation with major shareholders over the pay package.
Hans Wijers also sits on the committee, he is the chairman of Heineken and also sits on the brewer's compensation committee.
It could be an uphill battle for the company, currently votes on executive pay in the U.K. are non-binding. The government is trying to curb excessive executive pay and is consulting a range of possible solutions including adding a disclosure much like the Dodd-Frank pay ratio rule, which would show the difference between the CEO's pay and that of the median employee.
Institutional investors, including Hermes Investments and Fidelity, have also put forward proposals for reforming executive pay.