His statement came at the RSP's 16th Foundation Day celebrations in presence of Rural Development Minister Pankaja Munde.
At the event, a video clip of Dutt was played in which he said: "I congratulate RSP National President Mahadev Jankar, my friend and my brother. If I would have been here, I would have come."
Later, addressing the gathering at Shivaji Park, Jankar claimed: "Just now you heard the bytes of big boss...big brother. Sanjay Dutt has given September 25 day to join (RSP). He is in Dubai (today). Had he been in Mumbai, he would have definitely joined us."
In the past, on May 1, 2016, Dutt - released from jail after serving his sentence in the 1993 serial blasts case - had attended a BJP function at Dindoshi in north Mumbai, and speculation went rife that he would join the ruling party.
He had also urged the BJP to improve its tally in the next Lok Sabha elections, a fact viewed with trepidation by the Opposition Congress, since his late actor-parents, Union Minister Sunil Dutt and MP Nargis Dutt, and sister Priya Dutt had been diehard Congress' supporters since decades.
Jankar added that the RSP's influence had grown in the state and in next assembly elections, it would seek to contest at least 57 seats from the BJP.
An engineer hailing from the backward Dhangar community, Jankar was born in a poor family in Mann taluka of Satara district and was elected MLC with help of BJP-Shiv Sena.
Later, he told media persons that the party would expect at least 14 seats from the BJP given the (RSP)'s growing clout.
( With inputs from IANS )