Welshman Giggs, 43, was interviewed twice prior to Bradley's appointment as the successor to Francesco Guidolin in October.
They are all chasing the huge rewards available to winners, with accountancy firm Deloitte forecasting that last season's surprise champions Leicester City, owned by Thai businessman Vichai Srivaddhanaprabha, will enjoy revenues of at least £155m in the 2016-17 financial year, regardless of this season's performances.
Bradley was relieved of his position on Tuesday after a humiliating 4-1 defeat by West Ham left them second bottom and four points from safety.
Harry Redknapp says whoever takes over at Swansea will have a "tough" but not "impossible" job of keeping the side in the Premier League. Hiring the former Wales worldwide would certainly gain back parts of the fan base who disagreed with the hiring of Bradley three months ago. "It doesn't feel good, but sometimes in football you have to fight when everything is going against you".
The manager on his part is happy with his team's achievement, though he insists that a clean sheet would have been nice.
As the Mourinho regime commenced, Giggs then made his own personal Brexit from Manchester United after his 29 years of service with the club.
The difficulty was not lost on Bradley when he took the job.
"Personally, I have nothing but praise for Bob".
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A Mexican celebrity, Gael Garcia Bernal, even made a parody video of Crescencio's honest mistake. In it, he claimed "everyone" was welcome to attend, promising bands, a meal and the horse race.
"I received no xenophobia with the players I worked with every day, from the staff inside the club that I worked with every day, from the media here that paid real attention, got to know me through the press conferences, " he told BBC Radio 5 Live.
Swansea City are keen to have a new manager in place by Monday, as Wales boss Chris Coleman and Ryan Giggs appear to be the leading candidates.
The Swans next three matches will prove pivotal in their season - against Bournemouth, Crystal Palace and Hull City.
First team coaches Paul Williams and Alan Curtis will be in charge while the search continues for Bradley's replacement.
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Bradley believes Swansea City supporters need to get behind the team if they are to turn their fortunes around.
Meanwhile, former Chelsea defender Mario Melchiot believes Alan Pardew is the right man for the job at the Liberty Stadium because of his top-flight experience.