Across Scotland, more than 7,000 fans have backed the idea, forcing a parliamentary debate to take place in the next few weeks, though the issue will be decided by the Scottish Government.
As of last Friday, 690 people in Fife's five Westminster constituencies had signed the petition, among almost 200,000 across the UK.
In Dunfermline and West Fife it was signed by 229 people, in North East Fife by 98, in Ochil and South Perthshire by 81, in Kirkcaldy and Cowdenbeath by 164 and in Glenrothes by 118.
The petition on the UK Parliament’s website has gathered 197,000 signatures already, meaning MPs in Westminster will have to debate the matter, and that session is now confirmed for November 9.
Petition creator Ashley Greenwood said football is a "powerful tool" that brings a range of economic and social benefits, adding: "Football can be associated with passion, emotion, excitement and dedication across the community.
"I fear that smaller clubs in particular will go out of business, leading to a devastating effect on people."
Two Scottish Professional Football League games were allowed to take place in early September, with just 300 socially-distanced spectators allowed in, before further plans were put on hold amid soaring numbers of coronavirus cases across the country.
A Scottish Government spokesman said: “We recognise this has been an enormously challenging time for football and other spectator sports and we appreciate the support of supporters, clubs and authorities over recent months to help us tackle the virus.
“We are working in partnership with the football authorities and clubs to ensure the necessary public health measures are in place to open up grounds to a limited numbers of supporters once it is safe to do so.
"However, with rising cases, there is no immediate prospect of supporters returning because the virus has not gone away and we all need to keep working to protect the NHS and public services and help keep people safe.”
UK digital, culture, media and sport secretary Oliver Dowden admits there is a growing sense of frustration at the ban on live crowds at sporting events, especially now fans can see their opposite numbers in other countries at Champions League games being broadcast by BT, but insists there can be no change until the spread of coronavirus is curbed.
Speaking at a meeting of Westminster’s digital, culture, media and sport committee, Mr Dowden said: "There is very clear evidence from the scientific community that at this stage of the disease, with rapidly rising infections, we should be imposing restrictions, which we are, not further easements.
“We are doing things that are positively hateful, but the reason we are doing it is to secure public safety.”
Though Mr Dowden, MP for Hertsmere in Hertfordshire, gave no timeline, he did add that the emergence of a vaccine, on-the-day testing or further control of the virus could all help enable the return of fans to sporting events.
Responding to a question at a recent first minister's questions session at Holyrood, Nicola Sturgeon said: “We’ll continue to discuss with the football authorities how we can best support them in that.
“All of us, me included, want to see football, all sport and all of society get back to normal just as quickly as we possibly can.”
1. 14-12-2019. Picture Michael Gillen. FALKIRK. Falkirk Stadium. Falkirk FC v Raith Rovers FC. Matchday 17. SPFL Ladbrokes League One. Raith Rovers' fans on tour.
Raith Rovers fans watching their team play Falkirk last December. Picture Michael Gillen. Photo: Michael Gillen