The Briton is one of Williams's longest-serving members, having originally joined the Grove-based outfit as race mechanic to Nigel Mansell in 1985.
He moved up through the ranks and first took on the race team manager role in 1995 - staying in that position for 10 years before taking a factory-based job so he could spend more time with his family.
After returning to a travelling position as test team manager, Stanford took over the race team manager position full-time again in 2010.
It is understood that discussions between Williams and Stanford are ongoing to define his future role within the organisation.
Former McLaren technical co-ordinator Peter Vale has been appointed by Williams as its new race team manager.
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