The friendly, announced back in February, is not on a FIFA fixture date. Earlier in the month, Ukraine eased past the United States 2-0 in an exhibition match shifted from Kharkiv to a Mediterranean island nation 600 miles to the south to the political unrest in Kiev.
Preparing for their seventh straight World Cup appearance, the Americans opened their 2014 schedule with a 2-0 win over South Korea on Feb. 1. The U.S. is planning home exhibition games for May 27 against Azerbaijan , June 1 vs. Turkey and June 7 against Nigeria before leaving for the tournament in Brazil.
"Everyone knows the clock is ticking," said Klinsmann in a released statement on Wednesday. "This is a huge opportunity for our players to show where they are at and to make their case. We expect them to give a really strong performance against a Mexican team that is now basically coming back on track. They need to prove now that they badly want to go to Brazil."
Absent for the game will be top goalkeeper Tim Howard, who plays for Premier League club Everton. Bayern Munich's Green has been released by his club to participate in what could be his first match representing the United States.
Midfielders: Kyle Beckerman (Real Salt Lake), Michael Bradley (Toronto FC), Brad Davis (Houston Dynamo), Landon Donovan (LA Galaxy), Maurice Edu (Philadelphia Union), Luis Gil (Real Salt Lake), Graham Zusi (Sporting Kansas City).
Forwards: Clint Dempsey (Seattle Sounders FC), Julian Green (Bayern Munich), Eddie Johnson (D.C. United), Chris Wondolowski (San Jose Earthquakes).
Information from The Associated Press was used in this report.