The American, 27, plans to be ringside next Friday when Burns meets WBA super-lightweight challenger Relikh.
"We were pretty much there in terms of the deal to fight Broner," said Hearn.
"But because of issues out of the ring we all decided to fight Relikh and try and clear the mandatory before securing the fight against Broner in December."
Broner is a former four-time world champion and was last in action in April when he stopped Londoner Ashley Theophane in Washington, taking his record to 32 wins from 35 fights.
"Adrien contacted me this week and said he is coming to Glasgow on 7 October to watch the fight," added Hearn.
"If Ricky defeats Relikh I expect that fight to get made without any problems."
Ricky Burns will take on Adrien Broner in Glasgow in December if he defends his world title against Kiryl Relikh, says promoter Eddie Hearn.