Sobotka was scheduled to tender his resignation to Zeman on Thursday afternoon.
The leftist Sobotka said Tuesday he was standing down amid a high stakes row with his billionaire Finance Minister Andrej Babis, a popular centrist rival tipped to win elections later this year.
Government spokesman Martin Ayrer said in a statement that Sobotka would meet with Zeman later Thursday to "fix a date" to submit his resignation.
The move was likely to come after Zeman returns from a May 11-18 visit to China, said Interior Minister Milan Chovanec, a member of Sobotka's CSSD Social Democratic party, due to travel to Beijing with the head of state.
"The prime minister will present the president with an analysis summing up the serious doubts and questions that have been left unanswered about the taxes and business dealings of Finance Minister Andrej Babis," Ayrer added.
The head of the centrist ANO party and the second wealthiest Czech national, Babis has found himself under fire over his purchase of tax-free bonds issued by his mammoth Agrofert farming conglomerate.
Sobotka has cast doubt on the way Babis had raised money to buy the bonds and insisted that a finance minister fighting tax evasion should not benefit from tax loopholes. Babis has flatly denied any wrong-doing.
Babis is also the Czech Republic's most popular politician with a 56 percent approval rating, according to an April CVVM poll, compared to 39 percent for Sobotka in sixth place.
The Czech political scene has been gripped by debate for weeks over the fate of the three-party governing coalition comprising Sobotka's leftwing CSSD party, Babis's ANO and the small centrist Christian Democrats, which took office in 2014.
The next scheduled general election is set for October 20-21, three months ahead of a presidential poll.
Analysts in Prague said a snap election was unlikely to be called during the summer.