Rangnick has been in interim charge of Manchester United since December and is set to leave his role at the end of the season.
The German has committed to taking up a consultant’s role at Old Trafford over the summer, but it has been claimed that he has other offers.
According to Austrian daily Kurier, Schottel flew to Manchester last week to have a meeting with Rangnick.
He was in Manchester in the capacity of the Austria sporting director and the talks were centered on Rangnick becoming the head coach of Austria.
The Austrian FA want the current interim Manchester United boss to take charge of the national team.
Austria have not qualified for a World Cup since their last appearance in 1998 and want to have a fresh start under a new head coach.
The FA are pushing for Rangnick to take charge of the side ahead of the European Championship qualifiers.
For the moment, he is committed to becoming a football consultant at Manchester United, but now he has the prospect of becoming the coach of a national team over the summer.
