The offer came a day after Sena hinted at a truce with BJP following bad blood between the two parties in the run-up to the election.
"BJP has offered to give mayor's post to Sena for four years and one year to itself (in KDMC). While the chairmanship of the Standing Committee is to be held by BJP and Sena for three and two years, respectively," a senior BJP leader said.
Alliance partners at the Centre and in Maharashtra, Sena and BJP had, however, separately contested the KDMC election with the cut and thrust of campaigning characterised by mudslinging.
While Sena emerged as the single largest party with 52 seats, BJP improved its tally handsomely to bag 42 seats. Sena is 10 short of the magic figure of 62 in the 122-member body.
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"We had extended support to four of the Independent candidates put up by the '27 Gaon Sangharsh Kruti Samiti' for the November 1 KDMC election," he said.
On the BJP's offer of sharing power, he said the party was at the same time engaging in horse-trading.
The election for the mayor's post is held by a secret ballot and, as per rules, should be held on November 11.
While the Raj Thackeray-led Maharashtra Navnirman Sena (MNS) won nine seats in KDMC, Congress and NCP won four and two seats, respectively.
While KDMC has 122 seats, voting took place for 117 seats as two wards had boycotted the polls while three corporators were elected unopposed.