The Scottish fighter was due to face IBF titlist Miguel Vazquez on March 16, but was left frustrated last week when the Mexican withdrew with a stomach virus.
It is the second time that an opponent has pulled out at late notice following Jose Ocampo's withdrawal in December.
According to reports, Burns has become disillusioned with life under Warren's promotion and could seek a termination to his agreement.
When asked if he would be interested in signing the 29-year-old to his growing Matchroom Sport roster, BBC Sport quotes Hearn as replying: "He's world class, so of course we'd be interested, but we do not speak to people who are signed to others."
Hearn last week confirmed the capture of British and Commonwealth super middleweight champion George Groves from Warren's company.