The talks for new episodes are said to be in the very preliminary stages, and it's far from certain that a deal will be reached, reports Variety.
Previously there were reports that the Fox network might pick up the project from its sibling studio.
UPDATE: Twentieth Century Fox TV has released the following statement, saying that the show will not continue on TBS:
"While we had hoped to find a way to produce additional episodes for TBS, in the final analysis we simply could not make the economics work without seriously undermining the artistic integrity of the series. As none of us, [series creator] Greg [Garcia] included, want the show to go out on anything but a high note, we regret that we must put to rest any speculation that Earl will continue. We are grateful to everyone at TBS for their enthusiasm for the series and wish to offer our heartfelt thanks to the cast and crew of My Name is Earl for their incredible work."
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