A campaign was launched to persuade local officials in Harrison's adopted hometown of Henley-on-Thames in Oxfordshire, England to erect a monument to the area's most famous former resident.
However, Harrison's widow Olivia, who still lives in the region, has spoken out against the plans, insisting a statue could draw hundreds of unwanted visitors to Henley-on-Thames.
Resident James Lambert, who has been spearheading the campaign, has now abandoned the bid and is backing Olivia's suggestion of a "community project" instead.
He tells the Bbc, "The statue could create problems of different types of fans turning up, the unwanted fans. Gauging the pulse in terms of Henley residents I think there was a lot of support.
"This petition wasn't tapping into the Beatles fanfare worldwide, it was much more to recognise George's contribution to Henley and the affection Henley had for him. It is slightly disappointing but you have to respect Olivia's wishes, as she still has a house in Henley, Friar Park.
"And I think the danger was it wouldn't just become a Henley acknowledgement of George's work but would encourage more people to visit Henley. I think what she's suggesting in terms of a community project would be great and it'll be very exciting to see exactly how this transpires."
Harrison died in 2001.