Should the mayor actually step down, he would be the sixth Christian Democratic state premier to walk from his job in the last year, and would leave Merkel looking increasingly isolated at the top of the party, according to Stern magazine.
Beust, 55, has been mayor of Hamburg for nine years, and has largely been popular, particularly after throwing out his own interior minister, Ronald Schill, who had tried to blackmail him over his homosexuality.
But the last few years have been problematic with the explosion in costs of building the Elbe Philharmonic, and increasing violence on the streets of Hamburg.
His coalition of CDU and GAL, the Hamburg Greens, has recently introduced a reform of the school system in the state, which is being challenged in a referendum on Sunday.
NDR television is reporting that Beust has already decided to announce his resignation a few hours before the result in order to make it appear independent from whatever is decided. A public statement is expected.
Rumours have been flying around Hamburg for days that his departure was becoming imminent, so he could have more time for his personal life after nearly a decade in the public eye.
Talk is already turning to who would follow Beust, with Interior Minister Christoph Ahlhaus seemingly the favourite, but Social Minister Dietrich Wersich has also made it known he would like the job.
The speculation has created uncertainty within the GAL, which was persuaded by the relatively liberal Beust to form the rare coalition with the conservatives.
“The Greens did not make a coalition with the CDU, rather with von Beust,” political scientist Hans Kleinsteuber told the local paper Hamburger Morgenpost.
“It would be dangerous for both parties should he resign.”
The paper reported on Saturday that many Greens would have difficulty working with Ahlhaus at the head of the state government as he is regarded as a hardliner.
“He would have to radically change his style as mayor,” the paper quoted an anonymous GAL leader saying. “If he were to continue to play the agitator the coalition would fall apart.”
Merkel already lost Thuringia's CDU premier Dieter Althaus last year after a poor election result. He was then followed Günther Oettinger from Baden-Württemberg, who became an EU commissioner. Roland Koch from Hesse recently stepped down, as did Christian Wullf from Lower Saxony, who was made federal president. Jürgen Rüttgers was voted out of office in North-Rhine Westphalia in May and stepped down last week as caretaker premier.