"I assume that we will reach a good solution tomorrow," the source told reporters, speaking on condition of anonymity, a day before EU trade ministers meet in Luxembourg to try to overcome objections from France.
That solution would "accommodate different sensitivities", the source added.
France argues that its prized "cultural exception" should be excluded in the free trade talks with Washington, fearing the loss of its cultural assets to US influence and Hollywood's dominance of the film industry.
French Prime Minister Jean-Marc Ayrault threatened Wednesday to veto the talks.
"France will oppose the opening of the negotiations if culture and the cultural industries are not protected, are not excluded," Ayrault told the French parliament, saying this was a "crucial issue".
Washington and Brussels hope the EU-US Transatlantic Trade and Investment Partnership, which would be the world's largest free trade accord, will deliver a major boost to growth and jobs.