Richard Schaefer, chief executive of Broner's promoter, Golden Boy, confirmed at the weekend that he has been in discussions with counterpart Frank Warren, who looks after Burns' interests, with a proposal that the fight takes place in Atlantic City on February 16.
Broner, the World Boxing Council champion, is due to defend against Cuban Richar Abril on that date, but Schaefer stated that Burns is the preferred option, adding that the Scot would receive as much as £400,000.
But Burns has been advised by his manager, Alex Morrison to reject the offer to face Broner, given the high-risk nature of such a bout.
Warren also stressed that it will be up to Burns to make the call after confirming: "I have spoken with Richard Schaefer and the Broner fight is one of a number of possibilities. I will meet with Ricky next week to discuss the situation but he will be the one to decide."
Burns was not available to comment yesterday but Morrison claimed that the Scot should turn down Schaefer's initial offer. He said: "We are not going to take the fight with Broner unless there is a lot of money involved. Ricky would need to get a life-changing purse, at least half a million pounds, but there are a lot of issues to be resolved."
Morrison added: "My own feeling is that it is too soon. I want Ricky to have another fight first."
Burns should have been in action at the weekend, on the ExCel bill promoted by Warren in London, but his fight with Jose Ocampo was called off at just four days' notice when the Filipino challenger was mysteriously withdrawn last Tuesday.
No explanation was given for Ocampo being removed from the bill after he had been drafted in as a replacement for Norfolk's Liam Walsh, who was injured in a car crash.
Both Burns and Morrison were unhappy at the late call off and the fact that the champion was asked to box a meaningless 10-round international bout instead.
Warren later announced that Burns would return to the ring at the end of January, almost certainly in Glasgow with the 26th pencilled in as the likely date.
Two-weight world champion Burns has expressed a desire to have a unification bout in a bid to win a third title, but Broner, from Cincinnati, represents a huge challenge, especially with home advantage, given that he has so far proved unstoppable.
Broner has won 21 of his 25 fights by knock-out and the man nicknamed "The Problem" destroyed former WBC champion Antonio DeMarco, of Mexico inside eight rounds in Atlantic City last month to claim the crown.
He had previously succeeded Burns as WBO super-featherweight champion after the Scot relinquished the title to move up to lightweight and is regarded as one of the best pound-for-pound fighters in the world.