Stepping down on Wednesday, the outgoing Prime Minister Ivo Sanader said that his party - Croatian Democratic Union (HDZ) - had collected with coalition partners the signatures of 83 members of parliament for Kosor's candidacy as prime minister-designate.
Deputy Parliament Speaker Vladimir Seks told Croatian Radio that a majority of MPs, that is 83 of them, had asked Croatian President Stjepan Mesic to nominate Kosor as prime-minister designate.
Under the law on the government, the prime minister forwards his resignation to the parliament and if the highest law-making body accepts the resignation, it will dissolve the cabinet of the resigning prime minister. According to the make-up of the parliament and consultations conducted, the head of state should then nominate a person who enjoys the confidence of a majority of MPs as new prime-minister designate.
Kosor, born in Pakrac, on 1 July 1953, graduated from the law school of Zagreb University.
From 1972 to 1995 she was a journalist working for the Vecernji List daily and the Radio Zagreb.
In 1995 she became a representative in the Croatian Parliament as a member of the Croatian Democratic Union (HDZ) and she also became the party's vice president and a vice-president of the national parliament.
She again won a parliamentary seat in 2000, and two years later she was elected as the party's Deputy President.
Currently she is serving as Deputy Prime Minister and minister for the family and war veterans' affairs and inter-generational solidarity, to which she was appointed in 2003.
In the last presidential elections in 2005, the HDZ nominated Kosor as its candidate. Kosor faced off Stjepan Mesic in the then presidential run-off, but lost.
She speaks English and German.