The Tour de France is said to be inspiring many to take up the sport, with retailers reporting a marked rise in sales over the past three weeks while the race has been screened.
Cycling Scotland, the body for promoting the sport, also said it was anticipating a boom in interest.
Wiggins looks set tomorrow to become the first Briton to win the Tour while Mark Cavendish claimed the 22nd stage win of his career yesterday.
Scot David Millar has also won a stage on this year's Tour.
Ian Aitken, chief executive of Cycling Scotland, said: "Certainly, we've seen a steady growth in cycling's popularity over the last few years. If Bradley Wiggins does win this weekend the effect could be massive.
"Cycling Scotland's own cycling event, freshnlo Pedal for Scotland, has grown from having 1500 riders in 2005 to a massive 14,000 last year, and research shows participants are cycling more regularly as a result of taking part."
The Tour began on June 30 and its 20 stages will total 3497 kilometres by tomorrow's finish.
Wiggins' previous best was finishing fourth in 2009 – the same position as Scotland's Robert Millar achieved in 1984.
Wiggins finished 24th in 2010 and last year was forced to pull out with a broken collar bone but looks set to wear the leader's yellow jersey all the way to Paris this year.
Mr Aitken added that figures published by Sustrans Scotland showed that 4% of children now cycle to primary school and in some areas, such as Highlands and East Lothian, the proportion reaches as high as 10%.
In addition, more than 7% of Edinburgh residents now cycle to work – against the Scottish average of 2.3%.
Mr Aitken added: "These increases are driven by a range of factors, such as investment in cycle infrastructure and promotional measures, but you can't underestimate the effect that high-profile cyclists have on inspiring people.
"With a likely British success in the Tour De France, and the high expectations for the GB Olympic cycling team, this looks set to be an amazing summer for inspiring people to rediscover the joy of riding their bikes."
Scotland's four-times Olympic gold medallist, Sir Chris Hoy, has also expressed his hope that Wiggins' achievement will attract more people to cycling.
He said: "I have to pinch myself when I switch on the TV and I see Bradley in the yellow jersey. If he makes it to the finish line in Paris it will be one of the greatest achievements by a British sportsman ever – it's phenomenal."
He added: "Hopefully all the benefits of all the Olympic exposure for cycling and the Tour will encourage people to get out on their bikes."
Meanwhile, Evans Cycles, which has stores at Braehead and Edinburgh, credited the Tour for a spike in its sales.
A spokesman said: "We have seen sales of road bikes increase this month.
"Our sales have best improved in the price range of £700-£2000, which is around the value we would expect real cycling enthusiasts to spend.
"No doubt many consumers have been inspired by the success of Wiggins and all the other racers and therefore feel that they too can step up their performance by having the next level of equipment."
Former professional cyclist and general manager of Livingston-based Endura Racing, Brian Smith, said he hoped Wiggins's success would stoke Scottish passion for the sport.
Paisley-born Smith, said: "As a lifelong cyclist and fan of the sport it is fantastic to see. It's pleasing to me because I had a lonely furrow in my own cycling career in Scotland, but now we are seeing much more mainstream interest. It's something I would love to see more of."
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