Wright was scratched before Thursday's 3-1 loss to the Dominican Republic in Miami due to a rib injury that sent the Mets third baseman to New York to be examined on Friday, Team USA said.
He batted .438 with a grand slam and a tournament-leading 10 runs batted in for the U.S. and was replaced at third base on Thursday by Arizona Diamondback Willie Bloomquist.
Team USA manager Joe Torre was not optimistic that Wright would be able to return.
"I'm really not counting on it," Torre told reporters. "Whatever he has is going to take more than a few days, I would think."
Headley has been contacted and expressed interest in playing for the U.S. team should Wright be unable to continue and the Americans advance, the MLB Network reported.
Headley led the National League in runs batted in last season with 115, blasted 31 home runs and also snared the Gold Glove award as the league's top-fielding third baseman.
The U.S.-Puerto Rico winner will join the Dominican Republic, two-time reigning champions Japan and the Netherlands in the semi-finals.
The semi-finals of the 16-team tournament will be held on Sunday and Monday in San Francisco, with the championship game on Tuesday. (Reporting by Larry Fine in New York; Editing by Frank Pingue)