No-one disputes that the poster was based on AP's photograph
The Associated Press is claiming compensation for the use of one of its photographs to create the most iconic image of Barack Obama.
The red, white and blue portrait by Shepard Fairey appeared on thousands of posters and T-shirts and is now in Washington's National Portrait Gallery.
Lawyers for AP and Shepard Fairey are reported to be holding talks.
Mr Fairey's attorney says it was a case of "fair use", which allows exceptions to copyright law.
'Hoping for amicable solution'
The Los Angeles-based street artist has acknowledged that the image is based on a photograph taken in April 2006 by Mannie Garcia, a photographer on assignment for AP.
FAIR USE IN US LAW - KEY QUESTIONS
Purpose of the use: was the image used in a commercial or non-commercial way?
Nature of the copyrighted material: how creative or factual was the original?
Transformation of the work: was the original changed giving it new meaning or value?
Amount copied: how much of the original was copied and was it central to the original?
Effect on the market of the original: could it supplant demand for the original?
AP's director of media relations Paul Colford says that because it was an AP photograph, its use by Shepard Fairey "required permission" and AP should have been credited.
"AP safeguards its assets and looks at these events on a case-by-case basis. We have reached out to Mr Fairey's attorney and are in discussions. We hope for an amicable solution," he said.
However, Mr Fairey's lawyer, Anthony Falzone, said: "Fair use protects Shepard's right to do what he did here."
Fair use can, under certain circumstances, give the public a right to copy an author's work for the purpose of criticism, parody, or educational use without permission.
Georgetown University law professor Rebecca Tushnet told the BBC that while Mr Fairey clearly copied the photograph, it could be argued that what he took from it was the basic fact of Mr Obama's features, which do not have a copyright.
"If the case were to go to court, the creative elements of the photograph would have to be established in the first place," she said.
Shepard Fairey signing his Barack Obama Hope artwork
"There's a lot of transformation going on in Mr Fairey's image, and the photograph was pretty factual, so it could prove tricky for AP", she said.
Mr Fairey himself has not commented on the alleged copyright infringement.
Speaking in an interview with the BBC World Service before the copyright row erupted, he said he was more accustomed to making negative posters of politicians, but was inspired to create a positive image of Barack Obama when he heard him speak at the 2004 Democratic National Convention.
He was once arrested for flyposting the image.
"Being in the National Portrait Gallery feels like a pretty big coup," he said.