Senior BJP leaders Rajnath Singh and M. Venkaiah Naidu will meet Congress President Sonia Gandhi on Friday in a bid to evolve consensus on the presidential candidate even as opposition parties are said to be keen on a fight in the July 17 election.

Singh and Naidu, who are part of the three-member team constituted by BJP President Amit Shah for discussion with political parties on the presidential candidate, are set to meet Gandhi at her residence on Friday morning, sources said.

This will be followed by a meeting with CPI-M General Secretary Sitaram Yechury later in the day. Finance Minister Arun Jaitley, who is also part of the team is away in South Korea. He is scheduled to return only on Saturday morning.

The BJP has given no indication so far on who its candidate is but there is speculation around the names of External Affairs Minister Sushma Swaraj and Lok Sabha Speaker Sumitra Mahajan. The name of BJP veteran Murli Manohar Joshi is also not ruled out in BJP circles since he is said to have the backing of RSS.

It remains to be seen whether the BJP team will put forward any name to Gandhi and other opposition leaders it would be meeting or talking to in the coming days, or whether the team would merely seek the support for a BJP candidate.

Sources in the opposition parties say that they are waiting for the government side to come out with the name of its nominee before they can finalise their strategy. Opposition leaders say that the choice of BJP candidate, even according to insiders, is known "only to (Prime Minister) Modi and God", to stress the point that it was Modi who was calling the shots on the issue. 

They feel that the government was only engaged in an exercise of consensus building for the sake of formality and, in fact, may not be keen on a consensus candidate.

They point to Naidu's statement a couple of days ago that the government has the mandate and the opposition should keep this in mind when talking about a presidential candidate. 

At the meeting of opposition parties on Wednesday, there were suggestions mainly from Left parties that they should put up a fight by fielding a candidate because it is an "ideological battle" with BJP. They feel the BJP might be keen on having someone with ideological moorings in the Rashtrapati Bhawan.

Should there be a fight, the Left parties are reportedly keen on fielding Gopalkrishna Gandhi, grandson of Mahatma Gandhi and former Governor of West Bengal. 

As part of BJP's outreach, Shah is likely to meet Shiv Sena Chief Uddhav Thackeray in Mumbai in seeking the party's support for the NDA nominee. The Sena, which has been having a cold war with BJP, has not voted with the NDA in the last two presidential elections.

The Sena has been pitching for RSS Chief Mohan Bhagwat for the top constitutional post and has also sought to know from the BJP why he (Bhagwat) is not acceptable. Bhagwat on his part has ruled himself out, saying he was not in the race.

Meanwhile, disgruntled BJP leader Shatrughan Sinha on Thursday yet again backed party veteran L.K. Advani as the most deserving candidate for the post of President, saying he was physically fit and has the ability to "understand the complexity of the Constitution".

In a series of tweets, Sinha said: "What Advaniji has, is the ability to understand the complexity of the Constitution and to take the right decision when needed without getting influenced by anyone, in the larger interest of the nation."

Sinha also said that Advani, who is 89, is "physically fit" for the post and no one has come out against his candidature. 

"No one is able to speak anything, be it from within or outside d party…no voice coming out against Advani's candidature.

"Advaniji is much more healthy and energetic than any of the young leaders. He has kept himself maintained so that he can take responsibility of the country," Sinha said.

Sinha has been sidelined in the party after Narendra Modi became Prime Minister of the country. He was also not inducted into Modi's council of ministers though he has claimed of long association with the BJP, since the time when the party had two members in the Lok Sabha. 

His proximity to Advani is said to be one of the reasons for being sidelined in the BJP.