Pervez Khattak, the secretary general of the party, and Asad Qaisar, the president of the party's Khyber-Pakhtunkhwa chapter, are in the race for the post of Chief Minister.
Khan's party has emerged the single largest force in the provincial assembly and is trying to cobble together a coalition.
A party spokesman in Peshawar had initially announced that Khattak would be the Chief Minister but the media reported yesterday that Khan was backing Qaisar for the position.
It said consultations were underway in this regard.
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Qaisar defeated Khattak in intra-party elections held this year and became the provincial president. He was president of the provincial chapter during 2008-2011.
Qaisar won elections to both a National Assembly and provincial assembly seat from his native Swabi district.
However, Khattak has claimed that he has the support of more legislators than Qaisar.
The party now appears divided into two groups over the issue of choosing a Chief Minister.
Khattak has been meeting leaders of other parties like the Jamaat-e-Islami and Qaumi Watan Party to discuss forming a coalition.
Following the meeting, Qaisar told the media that "Khan was very positive about" making him the Chief Minister.
Khan's party defeated the Awami National Party, which had ruled Kyber-Pakhtunkhwa for the past five years, in the May 11 polls.