Frank Warren has confirmed that Burns' fight against Mexico's Vazquez will headline his 'Rule Britannia' show at Wembley Arena on March 16.
Should Scotland's WBO champion come through the tough fight against Vazquez, who is ranked second at 135 pounds, he hopes to then overcome unbeaten WBA champion Broner.
Broner accused Burns of ducking a fight with him at super featherweight when the Scot moved up a weight category in 2011.
The American then offered to fight Burns at two days' notice last month when two of the 29-year-old's opponents pulled out of a lightweight bout at the ExCeL Arena in London, but he again turned down the opportunity.
Burns, from Coatbridge, insists he is not avoiding Broner and has promised boxing fans the much-anticipated fight will go ahead if he beats Vazquez in two months' time.
"For all the doubters out there who say I am avoiding him - I can assure you that the fight is going to happen," Burns said.
"Broner wants a fight, and it's one I have always wanted so it is going to happen.
"People were saying I was avoiding him, which wasn't the case at all. It was because I didn't have time to prepare.
"The talk of me ducking him does get to me. People have been giving me gyp.
"It's a fight that I want, but for now I can't really think about it. I have a very hard fight in front of me but I think I can win."
Burns has scored victories against Kevin Mitchell, Paulus Moses and Michael Katsidis since moving up to lightweight.
He had the chance to round off the year with another win, but Liam Walsh and Jose Ocampo had to pull out of December's clash in London.
The episode frustrated Burns, who had spent 11 weeks training for the bout, and he is looking forward to returning to the ring for what he predicts will be a tough fight against the Mexican, who has lost just three times in a 36-fight career.
"I am a fighter so I just want to get back to fighting," Burns added.
"I took a couple of weeks off after the bout was cancelled, but I have kept running.
"No-one knows more than me that this is going to be a very tough fight.
"He is one of the best in the division. He is a good technical boxer, very elusive. I don't see a stoppage in this. I will train and treat it as a 12-round war but if it is a boxing match then so be it."
Burns will now head off to Norway to train with Andreas Evensen - one of his victims at super-featherweight - in temperatures some 16 degrees Celsius below freezing.
He will then return to Britain before taking on Vazquez at Wembley, where he beat Katsidis two years ago to win his WBO title.
The Scot is convinced he will get a good reception in the English capital.
"It's always good when I fight down here," said Burns, who fought Graham Earl at the Wembley Conference Centre in 2005.
"It's like having home advantage. The last time I fought down here the crowd were excellent and I am sure they will be again in March."