Mr Gilani argues that the president, who denies cheap gucci bags the corruption charges, has immunity as head of state.
President Zardari is accused of using Swiss bank accounts to launder bribes.
The Supreme Court has said Mr Gilani defied a court order to write to the Swiss authorities and ask them to re-open the cases against Mr Zardari.
Mr Gilani is expected to argue that he received legal advice that it would have been unconstitutional to pursue the cases.
Mr Zardari says the charges against him are politically motivated.
In theory, the Supreme Court could convict Mr Gilani of the offences on Monday, but this is highly unlikely, reports the BBC's Aleem Maqbool from outside the court in Islamabad.
Legal arguments in the case are expected to take a few days at least, he adds.
Helicopters hovered overhead and hundreds of riot police were guarding the Supreme Court as Mr Gilani arrived, the AFP news agency reports.
Analysts say the case is part of a stand-off between the government and the judiciary, which many believe is being backed by the military as it pursues the case against the civilian administration.
In 2009 the Supreme Court overturned an amnesty dating from the period of former President Pervez Musharraf which protected President Zardari and hundreds of other politicians from being prosecuted for corruption.
In an interview with Al-Jazeera television gucci shoes cheap last week, Mr Gilani acknowledged he would have to stand down if convicted.
International rights groups have slammed the deportation but Home Minister Hishammuddin Hussein said Malaysia was not a safe haven for fugitives.
Jiddah-based newspaper columnist Hamza Kashgari, 23, was detained Thursday at the Malaysian airport while in transit to New Zealand. He was deported Sunday despite fears from rights groups that he may face the death penalty if charged with blasphemy over remarks he tweeted that many considered offensive.
"I will not allow Malaysia to be seen as a safe country for terrorists and those who are wanted by their countries of origin, and also be seen as a transit county," Hishammuddin said.
He said the deportation followed a request from the Saudi government. Allegations that Kashgari could be tortured and killed if he was sent back home are "ridiculous" because Saudi Arabia is a respectable country, he said.
Malaysian authorities also didn't receive any court order to halt the deportation, he added.
Lawyers representing Kashgari's family obtained a court order Sunday to try to keep him in Malaysia but he had been put on a plane back home by the time the order was issued.
Human Rights Watch slammed Malaysia's failure to respect human rights. It said Kashgari was kept incommunicado and denied access to lawyers and the U.N. refugee agency. Police also told lawyers that Kashgari was still being held after he already had been forced on a plane, it said.
"By its actions, the ministry of home affairs once again showed that it believes rule of law is whatever it says and that it is more than willing to be totally opaque in its operations to maintain its flexibility to do what it wants when it wants," said Phil Robertson, gucci bags cheap its Asia deputy director.
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