"DMK is a democratic party. For anybody to contest for president or general secretary's post, his name has to be proposed at the party's general council by majority and others have to abide by it," Karunanidhi told reporters after a meeting with the party's district secretaries here.
He said: "If I get such a chance in my personal capacity, then I would propose Stalin's name, as his name was earlier proposed by the party's general secretary and it will be like I am seconding it."
DMK general secretary K. Anbazhagan also said that if he makes a proposal and other members second it, then even the president (Karunanidhi) cannot refute it.
On whether he would contest for the party chief's post, Karunanidhi said: "I don't know whether I will be around till such time."
Referring to the recent media reports that he supports Stalin as his successor in the party, he said: "Can you show me that (how) Stalin would succeed me in the DMK?"
At a party function Thursday, the DMK chief said that Stalin would be the party's torchbearer after him to fight for the upliftment of Dalits.
Reacting to the media reports, Karunanidhi's elder son and union minister M.K. Alagiri Friday said the party was not a Hindu hermitage to name a successor to his father.
He said the party's by-laws do not allow announcing Stalin as the next leader of the DMK and the laws have to be followed.
On Alagiri's aspiration for the party president's post, Karunanidhi said that it would be decided at the general council meeting.
"DMK is a democratic party and any member can stand against Stalin," Karunanidhi said when asked whether he would ask Alagiri not to prevent Stalin's accession to the posts.
Karunanidhi said the party's internal elections would be over before the 2014 general elections.
Although from the same family, Alagiri and Stalin do not see eye to eye on some major issues concerning the DMK.
Alagiri has in the past made it clear that he would not accept anyone apart from Karunanidhi as the DMK leader and that he was ready to contest if there was a battle for the party leadership.
Karunanidhi, who has led the DMK since 1969, is now 88 years old and in poor health. The issue of who will lead the party -- one of India's oldest -- after Karunanidhi has been raised repeatedly.
Stalin became the treasurer of the DMK in December 2008. He became deputy chief minister of Tamil Nadu six months later when the DMK ruled Tamil Nadu.