Rangnick said he was not dealing with any potential Bayern interest at the moment, with his focus firmly on the Euro 2024 starting in Germany in June.
"There has been contact from the side of Bayern Munich and I have informed the Austrian Football Association," Rangnick told Austrian website 90 Minuten.
"We have a very trusting relationship. My focus is on the Austrian national team. We are focusing completely on the European championships."
"I feel very well here. At the moment there is no reason to intensively deal with this," he added.
Bayern, who had won the previous 11 league titles, missed out on this season's Bundesliga trophy with Bayer Leverkusen securing their first ever league crown five matches before the end of the season.
Tuchel, who had taken over Bayern just over a year ago, is leaving a year earlier than his contract after a disappointing domestic campaign that also saw them eliminated in the German Cup by third-tier Saarbruecken.
Bayern, however, are still in the running for one title, having reached the Champions League semi-finals where they face Real Madrid next week.
The 65-year-old Rangnick, who has coached Manchester United and RB Leipzig among others, said he would only deal with Bayern if and when the club made him an offer.
"If Bayern say 'we want you'. And then I would also have to ask myself 'do I really want this?'. If I want to do something else I will first discuss it with the Austrian FA," he said.
Austria face France in their opening Euro 2024 Group D match on June 17 and also play Poland and the Netherlands.
