Yanis Varoufakis "will be at the ECB tomorrow," a bank spokesman said on Tuesday, but declining to provide any details regarding the timetable or agenda of the visit or whether Varoufakis would meet ECB chief Mario Draghi.
The ECB's policy-setting governing council is scheduled to meet on Wednesday afternoon, the spokesman added.
Sources have told AFP that the meeting will vote on whether to keep open emergency liquidity assistance (ELA) to Greek banks.
Meanwhie, the Wall Street Journal reported that Varoufakis will travel to Berlin on Thursday to meet his German counterpart, for whom he expressed “great respect”.
“I only entered politics three weeks ago,” Varoufakis said. “Therefore, I remain optimistic on the possibility of an agreement.”
"We could envision an end to the Greek crisis starting from June," he added.
Varoufakis already paid a visit to his British counterpart George Osborne in London on Monday as he seeks to build support for a renegotiation of his country's €240-billion bailout.
And he was in Rome on Tuesday looking for support for his plans to make Greece's debt burden bearable.
In a flurry of diplomacy, Greece's new Prime Minister Alexis Tsipras phoned ECB chief Mario Draghi on Saturday and has booked meetings with Italian Prime Minister Matteo Renzi, French President Francois Hollande and European Commission President Jean-Claude Juncker this week.
Varoufakis has also said he feels it is "essential" to meet Schäuble, as Germany has shouldered the bulk of Greece's loans and is fiercely opposed to writing off any of that debt.
ECB holds key to saving Greece
Varoufakis hopes the ECB will continue to supply Greek banks with cash under the ELA programme while Athens battles with its European partners and creditors over the terms of its bailout.
Analysts said the ECB is, in fact, the linchpin to resolving Greece's new debt crisis and ensuring there is no so-called "Grexit" – or exit from the eurozone – that everyone fears.
The ECB's governing council must decide this week whether it will continue to allow Greece's government and banks to borrow money despite its junk-rated bonds.
If Greece is found to be in breach of its bailout conditions, special rules allowing it to continue borrowing will be cut off and the country could face a debt default.