Following the talks, which lasted just 20 minutes, ZZS board chairman Armands Krauze said his party will pursue discussions with other parties.
Krauze said that, should ZZS become an opposition party, it will vote against confirming a cabinet drawn up by JKP.
Prior to the election, Bordāns hinted that he'd prefer setting up a government without ZZS and the Harmony party.
The Harmony party won 23 seats at the 13th Saeima election, while the New Conservative Party and KPV LV each won 16 and are both considering their options to make up the new cabinet.
ZZS, which has been in power since 2016 and a coalition party since 2014, meanwhile had a poor run winning just 11 seats, down from the 21 in the previous election.