The Hellenic League club want the 52-year-old to play in a one-off cup tie against local rivals Patchway.
Winterbourne, who are managed by Grobbelaar’s former Liverpool team-mate from the 1990s, Nick Tanner, have now applied for his registration.
He last played for Northern League side Glasshoughton Welfare in 2007.
Tanner took over at the south Gloucestershire side less than two weeks ago.
He is hoping his friend of 20 years will find time to turn out for the Gloucestershire FA County Cup match on 5 December just three days before he is due to move to Canada.
Grobbelaar signed for Liverpool in 1980 and spent 14 years on Merseyside, winning six League titles and three FA Cup winner’s medals.
But he is probably best known for his wobbly-leg antics in the penalty shoot-out as Liverpool beat Roma in the European Cup final in 1984.
He also played for Crewe, Southampton and Plymouth, and had spells at a handful of other English clubs as his career wound down.
Grobbelaar has also coached and managed teams in South Africa and his native Zimbabwe.
However, his later career was tarnished by a long-running legal battle after he and others were accused of match-fixing by the Sun newspaper.
Although they were cleared of criminal charges in 1997 after two trials, Grobbelaar’s libel action against the Sun eventually went to the House of Lords – where his libel damages were reduced to £1 and he was ordered to pay the Sun’s legal costs.