Sources familiar with the situation say ABC News' chief Washington correspondent and the host of This Week has yet to accept the position, according to the paper.
The Post's sources also report that Stephanopoulos, 48, is eager to hold onto his job at This Week. The likelihood of the former Clinton aide juggling anchor duties on both programs is unknown.
If he accepts, Stephanopoulos would take over Diane Sawyer's co-anchor seat alongside Robin Roberts on the No. 2-ranked morning news show. News of the job offer follows the announcement from ABC's World News Tonight executive producer Jon Banner that current anchor Charles Gibson, 66, will step down Dec. 18. Sawyer, 63, is expected to take over the evening news broadcast as soon as the following Monday, Dec. 21.
However, if Stephanopoulos opts not to rise and shine with Good Morning America, sources tell the Post that ABC is also considering the program's current news anchor, Chris Cuomo.
ABC refused to comment on Stephanopoulos' reported job offer. His reps did not return calls for comment.