The former Sheffield Wednesday boss had been considered among the frontrunners for the Ibrox post since former Gers boss Steven Gerrard pulled out of the reckoning at the weekend.
That would appear to leave ex-Rangers defender and Socceroo Muscat as the outright favourite to succeed Russell Martin at the William Hill Premiership club.
Rohl, 36, may not have been leading the race but reportedly impressed the Rangers hierarchy during talks last week.
Previously an assistant manager at RB Leipzig, Bayern Munich and the Germany national team, Rohl steered Wednesday out of relegation trouble in the Championship in 2023-24.
The German then led the Owls to a 12th-placed league finish in his only full season as a manager before leaving the troubled Yorkshire club in July.
However, it is now understood he has decided against returning to the game with Rangers.
That could increase Muscat's chances of landing the job with the 52-year-old having also reportedly held talks with the Govan club.
The former Australia and Wolves defender is currently in charge of Chinese Super League side Shanghai Port, whom he guided to the title in 2024.
They are closing in on further glory this year as they sit two points clear with four games left. Their domestic season ends on November 22.
Speculation abounds that Rangers are lining up Neil McCann for an interim period in charge until his former Gers teammate is free to come to Glasgow.
Muscat won a domestic treble with Rangers in 2003 in his only season at Ibrox and, as a manager, he has also won titles in Australia and Japan with Melbourne Victory and Yokohama F Marinos respectively.
Meanwhile, the PA news agency understands there have been no new talks between Rangers and Gerrard.
It emerged on Saturday night the former Liverpool captain had chosen not to return to the club for a second spell.
Despite that, several bookmakers on Wednesday listed Gerrard, who oversaw Premiership title success in 2021, back among the favourites for the post.
Other names on the bookmakers' lists include former Manchester United player and boss Ole Gunnar Solskjaer, Hearts manager Derek McInnes, ex-Chelsea and West Ham boss Graham Potter and former Wolves manager Gary O'Neil.
Rangers return from the international break with a home game against Dundee United on Saturday.
The Light Blues are eighth in the table after seven fixtures, 11 points behind leaders Hearts and nine behind Celtic.
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