Sources in the party said that there was general consensus among the party leaders on the former finance minister's name for the top post.
They said majority of the BJP leaders feel that the party should form the government if invited by Lt Governor Najeeb Jung to take over the reins.
74-year-old Mukhi represents Janakpuri constituency and was elected to the assembly for seven consecutive terms.
The sources said that a final decision on who will be the chief minister in case the party decides to form government will be taken by BJP parliamentary board.
The BJP appears inclined to form a government in Delhi in the wake of Jung's report recommending that the single largest party be given a chance to come to power.
Meanwhile, hectic consultations were held by Home Minister Rajnath Singh with Delhi BJP chief Satish Upadhyay, Union minister Nitin Gadkari, BJP leader Prabhat Jha, who is the state in-charge in the party.
Moves in the ruling party came a day after Jung sent a report to President Pranab Mukherjee seeking permission to explore the possibilities of formation of a government by consulting the single largest party.
"The party will take a decision," the Home Minister told reporters after Gadkari, who is election in-charge of party affairs in Delhi, met him at the North Block.
In his report, Jung gave a detailed analysis of the political situation in the city and underlined the need to have an elected government in the city which is under President's rule since February 17 following resignation of the Aam Aadmi Party government which was in power for 49 days.     

BJP, the single party has 28 MLAs in a House of 70. Its ally Akali Dal has one MLA. BJP had won 31 seats but three party legislators Harsh Vardhan, Ramesh Bidhuri and Pervesh Verma were elected to Lok Sabha and had to resign their Assembly seats.
The Aam Aadmi Party had won 28 seats in its debut Assembly elections and had later formed the government with outside support from Congress' eight MLAs.

Latest News from State News Desk