"A socially polarising leader has polarised his own party. Can he run a smooth, stable and effective government at the centre? Think seriously," Kulkarni said in a tweet.
Kulkarni also told TimesNow news channel that L.K. Advani, who he said was the "tallest leader" in the party after Vajpayee, was not in favour of declaring Modi the BJP's prime ministerial candidate.
Kulkarni was part of the BJP's strategy team in the 2009 Lok Sabha polls and worked closely with Advani.
He also served as Vajpayee's speech writer and media adviser.
Moves are afoot in the BJP to appoint Modi as the party's prime ministerial candidate for the 2014 general election.