ESPN first reported owners will extend the offer to Selig Thursday during meetings in Phoenix, and the Milwaukee Journal Sentinel said the baseball chief is expected to accept and stay on after his current contract extension expires at the end of 2012.
The newspaper said Selig had voiced his intention to retire following the end of his current three-year deal.
"This is clearly it," he said in January 2008. "I can say this without equivocation."
But owners asked him to stay on longer and never formed a committee to find a replacement.
Should Selig, 77, accept the extension, he will have served as baseball commissioner for 22 years by the time it wraps up in 2014 -- longer than any commissioner in history except the first one, Kennesaw Mountain Landis.
Landis held office for 24 years before his death in 1944, the Journal Sentinel reported.