The Sharif brothers have asked the apex court to issue a judicial directive to the government. The directive will allow them to return home from their "forced exile" and permit them to take part in the forthcoming general elections.
A bench comprising Chaudhry and senior Judge M Javed Buttar will hear the petitions on August 9.
The petitions also mention a previous order delivered by the same court, on an appeal filed by Sharif, in March 2004. The order stated that the constitution gives all citizens the right to move freely and settle wherever they want.
"It is a settled proposition of law that the right to enter the country cannot be denied but a citizen can be restrained from going out of the country. The petitioner (Sharif) is a citizen of Pakistan and has a constitutional right to enter and remain in the country," said the 2004 order.
The brothers also accused the government of "brazenly violating" the order by preventing them from returning to Pakistan.
Nawaz Sharif, along with his family members, was exiled to Jeddah in 2000. The Musharraf government claims that Sharif's exile was part of a deal with the former prime minister and the Saudi royal family.
Sharif, who later moved to London, claims that he was forcibly deported.