The Football Association is seeking a replacement for Sam Allardyce, who left the role on Tuesday following the emergence of secretly-filmed video footage which showed him making a number of controversial remarks.
Germany general manager Oliver Bierhoff, a close friend of Klinsmann, claimed in July that his former international team-mate was in line to succeed Roy Hodgson.
On that occasion Allardyce was chosen by the Football Association for a reign which lasted just 67 days.
Klinsmann is again one of the frontrunners with bookmakers to land the job - but the 52-year-old has insisted his current focus is the United States' forthcoming World Cup qualifying match against Mexico.
The former Tottenham striker tweeted: "No truth to the rumors regarding England" - adding on US Soccer's official website: "Our entire focus is on November 11, when Columbus will rock."