Morgan announced this week that he will not be returning to America's Got Talent next season in order to focus on his CNN series.
An insider has claimed that America's Got Talent have already begun negotiations with Stern and are considering moving the show to New York to better fit the radio host's schedule, according to The Wall Street Journal.
Stern would reportedly be paid $15m (£9.4m) per year to join America's Got Talent, but it's not yet known how long the contract would run.
A rep for the Howard Stern Show host has not commented on the report.
Stern has previously discussed his love of America's Got Talent on his radio programme and also insisted that he would be a fine talent judge.
In December 2010, Stern signed a contract extension with SiriusXM to keep his controversial radio programme on the air for five years.
He is currently embroiled in a lawsuit with SiriusXM over unpaid stock bonuses that had allegedly been guaranteed in his previous contract.
America's Got Talent judge Sharon Osbourne has described Morgan's exit from the series as "really sad", adding: "He comes off as this pompous know-it-all British stiff ass but he's a really good friend."
America's Got Talent returns in the summer of 2012 on NBC.
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