Dortmund announced last week that Nuri Sahin has left the role of head coach following four consecutive defeats in all competitions.
Their U19s manager, Mike Tullberg, has been placed in interim charge and oversaw their 2-2 draw with Werder Bremen on Saturday.
However, Dortmund are working on a permanent successor to Sahin, with former Manchester United boss Rangnick in contention.
Florian Plettenberg of Sky Sport Germany has reported that there was a 'secret meeting' between club executives and the German.
Dortmund are said to have considered both an immediate or summer appointment of Rangnick as their new head coach.
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The 66-year-old, who is the current manager of the Austrian national team, appears more inclined to reject their offer though.
Rangnick has previous managerial experience in German football that includes stints at Stuttgart, Schalke and RB Leipzig.
His last club appointment came at United in 2021 when he was named as their interim manager following Ole Gunnar Solskjaer's exit.
Despite wins coming in three of his first five matches in charge at Old Trafford, Rangnick oversaw a sorry end to the 2021/22 campaign.
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A 4-0 defeat to bitter rivals Liverpool led him to liken the changes needed at United to 'an open heart operation'.
They finished sixth at the end of the season with 58 points, which remains as the lowest ever tally in their Premier League history.
Rangnick was due to stay at United within a consultancy role but this decision was reversed and he joined Austria in June 2022.
He guided them to Euro 2024, in which they reached the last 16, and his contract was subsequently extended through to the 2026 World Cup.
Austria will face Romania, Bosnia and Herzegovina, Cyprus and San Marino in their qualification group for the tournament.
Should Austria top or progress through the play-offs, they will qualify for the World Cup for the first time since 1998.