The coalition Modern Centre Party (SMC) and Pensioners' Party (DeSUS) intend to continue the talks, whereas New Slovenia (NSi) did not give a statement after the talks.
SMC leader Zdravko Počivalšek, whose party has ten MPs, said the talks were constructive and would probably continue.
DeSUS leader Aleksandra Pivec, whose party has five MPs, said her party was willing to continue the talks if other bigger parties were also willing to do so.
"If just one of the bigger parties taking part is against continuing the talks, then there is no point in continuing," she said.
Pivec indicated today's meeting with the SDS was testing the ground to see if there was readiness to continue, saying content or staff had been on the table yet.
Once the talks turn to actual policies, DeSUS will have many more demands, which will require reaching agreement, Pivec, outgoing agriculture minister, said.
Pivec, who has led the party for less than a month, also said that for DeSUS, an early election was still a priority.
The other parties did not comment on the SMC, DeSUS and NSi entering preliminary coalition talks with the SDS, which has 26 MPs in the 90-strong parliament.
However, outgoing Prime Minister Šarec said Počivalšek, whom he had offered a pre-election alliance when resigning, was "somehow losing trust in our eyes".
Responding to Šarec's statement, Počivalšek took to Twitter saying the best way to strengthen trust would be for Šarec to translate his TV offer into a concrete offer of cooperation.
Šarec, speaking to the Slovenian press during a visit to Brussels, said he was now even more convinced stepping down was the the right thing to do.
He sees the post-resignation developments as a "draught" exposing "what was happening and what was being discussed and agreed".
Now we can see "some ideas which we only sensed before", he said, probably in reference to the SMC leader saying some time ago he would be willing to take part in "a different coalition".
He insists that an early election is the best option to get out of the current political situation.
Šarec believes ideas about a new coalition are but attempts at "holding on to one's positions, (revealing) a fear of losing one's job".