German coach Ralf Rangnick insists there has been no fresh approach from the FA over the vacant England job.
Rangnick, 58, is director of sports at Bundesliga side Red Bull Leipzig and was interviewed by the FA before the job was handed to Sam Allardyce in the summer.
Sky sources understand FA technical director Dan Ashworth - who tried to appoint him at West Brom in 2012 - was impressed with Rangnick and is keen to speak to him again about the role.
But Rangnick told Sky Germany on Friday: "At the moment there has been no contact - no approach.
"It's right that I received a phone call from Dan Ashworth a few days after the Euro 2016 finals. He wanted me to become the England national team coach.
"I went there and it was a good meeting. But on the one hand they told me that the board preferred an English coach."
Rangnick, a fluent English-speaker, took Schalke to the Champions League semi-finals in 2011, where they were beaten by Manchester United.
Since his first managerial role in 1983, he has managed the likes of Stuttgart, Hannover 96, Schalke twice, Hoffenheim, Red Bull Salzburg and took RB Leipzig to the Bundesliga last season.
Gareth Southgate is in temporary charge of the national team, and FA chief executive Martin Glenn has said he is a "genuine contender".
Glenn also said that Arsenal manager Arsene Wenger, who on Friday revealed he would be prepared to manage England "one day", would "fit the criteria perfectly".