According to ESPN, former Tottenham striker Jurgen Klinsmann has no interest in becoming the new Aston Villa manager.
Lambert's side had scored just 12 goals in 25 games this season, and having gone without a win in ten games, they now lie in the relegation zone.
Owner Randy Lerner now needs to make a swift appointment, with just 13 games remaining of the Premier League campaign.
The likes of Tim Sherwood and Neil Lennon have been touted as possible replacements for Lambert, despite their lack of Premier League experience.
Another name mentioned in the conversation is Klinsmann, who is no stranger to English football having had two spells with Spurs as a player, scoring 39 goals in 68 games for Tottenham.
The German is currently the manager of the United States national team, and guided them to the last 16 of the World Cup, despite encountering a tough group alongside Germany, Ghana and Portugal.
ESPN believe that American owner Lerner is a big fan of Klinsmann's work with the States, and had considered making a move to bring him to the Premier League as Lambert's replacement.
However, they also report that Klinsmann has no interest in leaving his role with the USA, and wants to take the country to the 2018 World Cup in Russia.
That would leave Villa and Lerner heading back to the drawing board, which could well leave Sherwood as the frontrunner.