Mulayam Singh Yadav: Waiting for the invitation
The leader of the party, Mulayam Singh Yadav, met the state's Governor, Vishnukant Shastri, in Lucknow on Wednesday to make a formal request.
The Samajwadi Party has emerged as the largest party in the state in elections held this month.
But it failed to secure an overall majority.
Polls in the state were held along with three other states - Punjab, Uttaranchal and Manipur.
The results were a boost for the main opposition Congress party which has won two states and emerged as the largest party in Manipur.
Search for allies
Mr Yadav told journalists that he should be invited to form the government in Uttar Pradesh and given at least a month to prove his majority in the house.
The Samajwadi Party secured 145 seats in the 403-member state assembly - 57 seats short of an overall majority.
An alliance with the number two party - Bahujan Samaj Party or the ousted Bharatiya Janata Party is unlikely because of ideological differences and political rivalry.
There are reports that party leaders are desperately trying to garner support of some smaller parties and independent legislators.
Hung assembly
In the north eastern state of Manipur, the Congress party has formed a coalition with three other parties in a bid to form the state's next government.
The new alliance with the Nationalist Congress Party, the Manipur State Congress Party and the Communist Party of India has been named the Secular Front.
Together the three parties hold 32 seats, more than half of the 60 seats in the assembly.
The state Congress party chief, O Ibobhi Singh, will head the Congress legislature party and if the four-party coalition forms the government, he is likely to be the chief minister.
Formation of the new governments has already begun in Punjab and Uttaranchal where the Congress party won the polls.
A new chief minister has been sworn-in in Punjab and the party is due to announce the name of its leader in Uttaranchal.