Varoufakis said on Twitter that he found the rumours "somewhat amusing."
Every time the negotiations heat up, some new rumour of my resignation, demise etc. springs up. Somewhat amusing…
— Yanis Varoufakis (@yanisvaroufakis) March 27, 2015
Under the headline “Is the Greek minister about to save himself?” – a pun on the financial savings which Varoufakis' embattled government needs to enact – Bild claims to have obtained the information from Greek government sources.
“It is only a matter of time before Varoufakis goes,” a government insider told the paper. “That is already fact. It will also make relations with the EU and especially Germany easier.”
Varoufakis took up the post of finance minister on January 25th this year and has been leading negotiations on Greece's debt repayments with the EU and other financial lenders.
Relations with Germany, the key lender within the EU, have been severely strained over the past several weeks. The personal relationship between Varoufakis and his German counterpart Wolfgang Schäuble is said to be particularly bad.
On Wednesday during a Greek national holiday Varoufakis was having his photo taken with supporters, with one telling him “Keep doing what you're doing.”
“Don't just support me now. Support me when a break comes up,” he is reported to have replied, intensifying speculation.
Bild claims that in Athens Varoufakis is already considered damaged goods, saying the German outrage over his middle finger gesture and his arrogant demeanour in Brussels have damaged his relationship with prime minister Alexis Tsipras.
The right-wing tabloid has long sought to discredit the Greek finance minister, recently naming him the “lying minister” in reference to a video which apparently showed Varoufakis “giving the middle finger” when talking about Germany.
Varoufakis denied making the action, in what became known as the “stinkefinger affair.”
Bild is also strongly opposed to Greece's left-wing government. In February it ran a campaign to oppose further financial assistance to the economically struggling country.