The intra-court appeal is expected to be filed after a few days, media reports said.
"We are in the process of preparing the appeal which may take a couple of days more and (it) will be filed instantly afterwards," an unnamed associate of Aitzaz Ahsan, Gilani`s lawyer, told the Dawn newspaper.
Another member of Ahsan`s team told The News daily that the appeal could be filed by Wednesday or Thursday.
A seven-judge apex court bench last week summoned Gilani to appear before it on February 13 for framing of contempt charges for failing to act on its order to reopen graft cases against President Asif Ali Zardari.
Gilani had personally appeared before the bench headed by Justice Nasir-ul-Mulk when it first took up the contempt case on January 19.
Since December 2009, the Supreme Court has been pressuring Gilani`s government to reopen cases of alleged money laundering against Zardari in Switzerland after striking down the National Reconciliation Ordinance, a graft amnesty passed by former President Pervez Musharraf.
Zardari and his late wife, former Prime Minister Benazir Bhutto, have been accused of laundering about USD 12 million in Swiss banks after they allegedly accepted bribes from firms seeking customs inspection contracts in Pakistan in 1990s.
Gilani`s legal team has only a week to file the appeal because the Premier has been summoned on February 13. When the appeal is filed, it is expected to be put up before a bench comprising the remaining nine judges of the Supreme Court.
Soon after the apex court had announced its decision to charge the Premier with contempt on February 2, Gilani`s lawyer Aitzaz Ahsan had said he would suggest to the Prime Minister to appeal the order.
Ahsan subsequently briefed Gilani and other leaders of the ruling Pakistan People`s Party on the legal implications of the court proceedings. Under the law, the apex court can suspend the order being challenged till the disposal of the appeal.
If the decision on indicting the Prime Minister is not suspended or stayed, then both the contempt case and the appeal will be heard simultaneously.
Legal experts have said that if Gilani is convicted, he could face up to six months in jail and be disqualified from holding public office.
There is also the possibility that his sentence could be pardoned by the President though his conviction would stay on record, making him ineligible for holding public office for five years, the experts said.