State BJP leadership maintained the party's central leadership will take a call on the matter.
However, Chief Minister Rupani seems to be a front-runner to retain the job.
Sources in the BJP here said the party was likely to stick with Rupani.
BJP president Amit Shah had said during the campaign that the party was fighting the election under Rupani and Deputy Chief Minister Nitin Patel.
But due to the BJP's narrow win, the central leadership may think of changing the CM, they said, adding everything is in Prime Minister Narendra Modi's hands.
Besides Rupani, the other names doing the rounds for the top job are those of Patel and Mansukh Mandavia, a Rayja Sabha MP from Gujarat who is a member of the Narendra Modi government, the sources said.
Mandavia hails from the Patidar community.
Asked who will be the next chief minister, Gujarat BJP president Jitu Vaghani evaded a direct response, saying the name will be known soon.
"Talks are underway about the date on which our legislators would meet to select their leader (the next CM). We will inform you soon.
Earlier, Rupani had said the party's parliamentary board will take the final decision.
Asked who will be the next chief minister, Rupani had told reporters, "The BJP fought this election with my face. But the final decision will be taken by the party's parliamentary board."
December 25 is the likely date for the swearing-in of the new ministry as it is the birthday of former prime minister and BJP stalwart Atal Bihari Vajpayee, the sources said.
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