"The proposal for the prime minister-designate can be expected within 30 days, which is the deadline envisaged in the rule book, " Drnovsek told reporters in parliament after he held a speech before new MPs in the Drzavni Zbor on Friday.
He added that he hoped the new stable government would be formed and said he would not wait for the final deadline to give his proposal for the PM-Designate.
The fourth Slovene parliament convened for the first time on Friday morning.
Addressing MPs who won seats at the 3 October elections, President Drnovsek called on them to form a stable government as soon as possible.
He said, among other things, that the forthcoming period would be calmer after the previous parliaments adjusted the national legislation to the EU standards. The head of state said that Slovenia was now facing many challenges in the European Union after it joined the European bloc earlier this year.
The 90-seat parliament consists of representatives of seven political parties.
The Social Democratic Pary (SDS) led by Janez Jansa, which won 29.8 percent of the vote, holds 29 seats. The Liberal Democrats of Slovenia (LDS), led by the outgoing Prime Minister Anton Rop, won 22.8 percent of votes and it holds 23 seats in the Drzavni Zbor.
The other five parliamentary parties are the Joint List of Social Democrats or ZLSD led by Borut Pahor with 10 seats, the New Slovenia or N.Si. of Andrej Bajuk with nine seats, the Slovene People's Party or SLS led by Janez Podobnik with seven seats, the Slovene National Party or SNS of Zmago Jelincic with six seats, and the DESUS pensioners party with four seats.