BMW New Zealand spokesman Paul Sherley told the Herald WIlliams contract remains unchanged but the company is reviewing his role.
"We take on board all customer complaints and consider them very seriously," Sherley said.
"We're looking at the best way we can utilise him in his capacity, as we do with each of our ambassadors."
One of Williams' tweets which has drawn criticism was of him doing a one-fingered salute - a Muslim gesture which has been adopted by some Isis soldiers.
New Zealand Muslim Association president Ikhlaq Kashkari said he was not aware of the salute.
He also didn't know Menk and Bham so couldn't comment on them, but in general, he supported Williams.
"Williams is a great sportsman for New Zealand and the Muslim community are right behind him.
"We are an inclusive community, though, and never support discrimination."
It was announced in October that Williams would be a brand ambassador for BMW in New Zealand.
As part of the partnership the rugby star received his own BMW X5 vehicle worth $161,000.
BMW group New Zealand manager Florian Renndorfer said at the time the company was "very delighted" to have Williams as an ambassador.
The appointment came after the brand dropped Williams in 2007 following a string of off-field controversies involving the then 22-year-old rising star.
There is currently no mention on BMW's website of Williams, despite profiles on other brand ambassadors, shoe designer Kathryn Wilson and chef Josh Emmet.
Williams could not be reached for comment.
