Celebrations erupted across the tiny West African nation last week when Mr Jammeh unexpectedly conceded defeat after the elections commission announced the victory of opposition candidate Adama Barrow.
However, in a dramatic U-turn the former coup leader rejected the outcome of the election and called for fresh polls, citing "serious and unacceptable abnormalities".
The move drew condemnation from the United Nations, African Union, European Union and the United States.
The ruling Alliance for Patriotic Reorientation and Construction (APRC) said it was preparing a petition "against the flawed decision of the Independent Elections Commission" in a statement broadcast on state TV late on Saturday.
The deadline for submitting a challenge to the court is Tuesday.
There is no sitting Supreme Court in Gambia, though there is currently a chief justice, who is Nigerian. In order to hear Mr Jammeh's complaint, legal experts believe at least four other judges must be hired.
Mr Barrow, who has pledged to serve as a transitional leader and step down after three years, said Mr Jammeh had no constitutional authority to reject the poll results.
The residence in the capital Banjul where Mr Barrow was staying on Sunday was surrounded by around 30 unarmed supporters who said they were providing security after the police and military declined to protect him.
Banjul was calm though armed soldiers were visible in the streets and manning checkpoints on some roads in the city. The head of the Gambian army pledged allegiance to Mr Barrow last week.
Omar Jallow, head of the People's Progressive Party, which backed Mr Barrow in the election, said Mr Jammeh's actions were "nothing more than a coup d'etat."
"We will not accept anything less than Adama Barrow being sworn in ... We will not take this lying down," Mr Jallow told Reuters.
Mr Jammeh, who seized power in a bloodless military coup in 1994, has long been accused of overseeing a government that imprisons, tortures and sometimes kills its opponents, according to human rights groups.
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