"If they (the BJP) propose a name who believes in the Constitution, who understands it and believe in its propriety, then there can be a consensus. We will talk," the Rajya Sabha member was quoted as saying to news agency Press Trust of India.
Asked to elaborate, he spoke of "love jihad" and "ghar wapsi" (re-conversion of converted Muslims to Hinduism), two issues, which, he said, was against the Constitution.
"In their three years of rule they have done things outside the Constitution, like 'love jihad'. Where is it written in the Constitution?" Mr Yadav was quoted as saying by PTI. The Constitution, he said, allows adults to marry people of their choice irrespective of caste and religion. "They have attacked this concept. They do nothing to remove caste barriers but practise 'ghar wapsi'. Opposition parties will support a candidate who believes in the Constitution," he was quoted as saying.
President Pranab Mukherjee's term ends in July and Prime Minister Narendra Modi has not asked him for a second term yet. The government is seen as scouting for a fresh face, even though no name has surfaced from the BJP camp yet.
Though Shiv Sena had proposed the name of Mohan Bhagwat, the chief of the BJP's ideological mentor Rashtriya Swayamsevak Sangh, it had not gained traction. Mr Bhagwat had rejected it and the BJP had remained silent. Recently, party chief Amit Shah said, Even if I have a name on my mind, it has to be discussed within the party first".
In view of the circumstances, the opposition is drawing up its own list. Congress chief Sonia Gandhi has spoken to all key opposition leaders to find an acceptable candidate and a meeting was held in Delhi last month. Mrs Gandhi's lunch last month was attended by leaders of 17 parties -- including the Left, the SP, the BSP, the RJD and the JD (U).