Barker, 30, has won his last two contests in four rounds since suffering his only loss to Sergio Martinez in October 2011 and the Londoner is now lined-up for a possible trip to Mexico in the summer.
“It’s early days but we have expressed our interest in Darren fighting Chavez following an approach from Top Rank,” Hearn exclusively told World Boxing News.
“I’ve discussed the fight with Darren and the team and it’s one we really fancy. Darren is back in full flow and these are the type of fights he wants now.
“Chavez is a quality fighter and they both share only one loss at the hands of Martinez so we’ll see how it plays out.”
27 year-old Chavez Jr. hasn’t fought since his loss to ‘Maravilla’ due to a ban for using marijuana, but it could be that the winner of any ensuing clash would then earn a rematch with Martinez in September.
Martinez tackles another Briton in undefeated Martin Murray on April 27 in Argentina, but the likelihood is that the winner of both fights will come together in the fall on US soil with the WBC title at stake.