Babis said last week that he would opt for a minority government including unelected technocrats after potential coalition partners balked at talks with the "Czech Trump", who is facing charges of EU subsidies fraud.
Campaigning on an anti-corruption, anti-euro and anti-migrant ticket, ANO won the October 20-21 general election, scoring 78 seats in the 200-member parliament.
It beat the right-wing eurosceptic ODS, the anti-establishment Pirates, the far-right, anti-Islam and anti-EU SPD and five other parties.
Party leaders in the EU state of 10.6 million people, where corruption is perceived as being rife, have shunned the 63-year-old Babis who faces fraud charges related to his Stork Nest farm.
The Slovak-born tycoon allegedly pulled the farm out of his sprawling Agrofert chemicals, food and media holding in 2007 to make it eligible for an EU subsidy granted to small companies, before eventually returning it to the holding.
Police said last week they would suspend prosecution after Babis regained immunity as a lawmaker in the election, but party leaders have continued to turn him down.
Czech media have suggested that Babis may have to rely on backing from the far-right SPD led by Tokyo-born entrepreneur Tomio Okamura to win a confidence vote in parliament.
They said the far-left Communists might help secure the confidence vote for Babis by leaving the chamber to reduce the quorum.
Okamura is the only party leader who has left the door open to cooperating with Babis despite the billionaire ruling out any formal alliance with him.
The new Czech parliament is set to meet on November 20, when the outgoing centre-left government of social democrat Bohuslav Sobotka, that also includes Babis's ANO, is expected to resign.
Zeman will then formally designate Babis as prime minister, but the ANO leader will have to win the confidence of a simple majority of legislators to hold onto office.
Czechs will choose their new president in January, with the outspoken leftwinger Zeman, a 73-year-old pro-Russia, pro-China, anti-immigration Babis supporter, competing for his second five-year term in that vote.