The presidential election is scheduled for August 6.
According to sources, some close aides of Prime Minister Sharif have told him that the office of President should be kept within the family by fielding 61-year-old Shahbaz for the presidential poll.
They are of the view that the PML-N needs a "stronger and most reliable person" for the office to better face a situation similar to that when Nawaz Sharif was ousted as Prime Minister by General Pervez Musharraf in a coup in 1999.
The sources said if consensus is not reached on Shahbaz Sharif, then former Sindh Governor Mamnoon Husain will be the PML-N's candidate for the slot.
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Pakistani authorities recently announced that the presidential poll would be held a month earlier than expected, a move seen as a bid to hasten the exit of President Asif Ali Zardari.
Meanwhile, the PML-N has asked all its parliamentarians and legislators not to leave the country and directed those who are abroad to return to take part in the presidential election.