Austria parted company with Franco Foda following their World Cup play-off defeat to Wales last month, meaning that they're now looking for a new boss to lead them into the upcoming qualifying campaign for the 2024 European Championships.
Reports in Austria claimed that the federation's sports director, Peter Schottel, flew to Manchester earlier this week in order to hold talks with Rangnick over the role.
The German coach is currently interim boss at Old Trafford, but is set to leave that role in the summer in favour of a consultancy position at the club.
While the nature of that role has not been fully revealed, speculation linking him with the Austria role is a non-starter, with the Austrian FA refuting the claims on Wednesday.
"'Clarification: There was no meeting between OFB sports director Peter Schottel and Ralf Rangnick, coach of Manchester United," the governing body posted on Twitter.
While Erik ten Hag and Mauricio Pochettino continue to be linked with the Man United role, the focus at the club is ensuring that Rangnick guides the club to a successful end to the season.
United currently sit seventh in the Premier League, and discussing Rangnick's time at the club, Nemanja Matic says that the players will continue to fight for the boss despite the poor results.
Matic told talkSPORT: "He is an experienced coach. We work very hard to be honest with him.
"Of course, everyone knows that at the moment we don't have the best results.
"He is trying his best and we are trying to follow his ideas. Only at the end of the season, when we see the table and see where we are, then we can speak more about this.
"At the moment, what I can say is that Ralf and his staff, and us as players, are doing our best."
Matic added: "The atmosphere? It depends on results. Of course, when you have good results the atmosphere is much better and everyone is happy.
"As you know we are not in the best position in the league and the atmosphere is not fantastic, but we have to stay positive and believe until the end because we want to finish in that top-four.
"The atmosphere in our dressing room will depend on that. If we finish top-four then it will be good for us, everyone will be… I cannot say happy, but satisfied.
"If we don't make that, it will be a very sad dressing room. "
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