Athawale, who heads the largest faction of nearly half-a- dozen RPI groups, said the offer was made by Sena chief Uddhav Thackeray.
"Uddhavji has requested me to form an alliance with his party and in return has offered me the position of Deputy Chief Minister if the Sena manages to form the government after the Assembly polls," he said.
Athawale said negotiations are still on with the Sena and BJP, who parted ways yesterday, and a final decision on an alliance would be taken as per the advice of party workers.
"I have demanded from the BJP a berth in the Union cabinet when it is expanded," the Rajya Sabha member said.
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The former state minister said several common demands have been placed by the RPI before both parties and it is for them to take a decision on accepting them.
Athawale said he has asked 25-30 candidates of his party to file their nominations tomorrow, the last day of submitting papers.
"But once our alliance is decided with a party, we will take some names back depending on the seat-sharing formula," he said.