The Gambia relies on foreign judges, notably from Nigeria, to staff its courts due to a lack of trained professionals
Jammeh's political party lodged a legal case on his behalf last month aimed at annulling his December 1 election defeat to opponent Adama Barrow, and triggering new elections.
"We can only hear this matter when we have a full bench of the Supreme Court," Chief Justice Emmanuel Fagbenle said, adding that the extra judges needed to hear the case were not available and could arrive only in May or November.
The Gambia relies on foreign judges, notably from Nigeria, to staff its courts due to a lack of trained professionals in the tiny west African state.
Fagbenle is the panel's only sitting judge, as the Supreme Court has lain dormant since May 2015.
The chief justice added that he would prefer the country to resolve its political deadlock through the mediation underway by a group of west African leaders, who are attempting to persuade Jammeh to respect the constitution and step aside.
"This is why alternative dispute resolution is important," he said. "We are now only left with the ECOWAS mediation initiative and the inter-party committee set up by government to resolve the dispute."
The inter-party committee is a UN-backed body aimed at resolving arguments between different Gambian political parties.
But Jammeh has made clear he will not go until his complaint is heard.
On December 20 he was broadcast on state television saying "unless the Court decides the case, there will be no inauguration on the 19 January. And let me see what ECOWAS and those big powers behind them can do."
The leaders from the ECOWAS regional grouping led by Nigerian President Muhammadu Buhari will return to The Gambia for the second time this week since the election to attempt to find a diplomatic solution to the crisis.
They were due to arrive Wednesday but the trip was delayed until Friday, Buhari's spokesman said, because Jammeh had asked for more time.
"Delay notwithstanding, the mandate of the ECOWAS will be accomplished," Garba Shehu said.
Nigeria's foreign minister said Monday the use of force remained an option if there was no movement in the situation. "Violence should be avoided but nothing is ruled out," Geoffrey Onyeama said.
Meanwhile an ex-minister and high-profile defector from Jammeh's government declared his support for Barrow, and said the Supreme Court case was an attempt to "subvert the express will of the Gambian electorate."
Former information and communication minister Sheriff Bojang fled to neighbouring Senegal on Monday after resigning.
Bojang said his conscience had overwhelmed him after Jammeh declared he would not step down at the end of his mandate.
As minister for two years he was Jammeh's mouthpiece for explaining the actions of the regime, including arbitrary detentions, activists' deaths in custody and a crackdown on opposition protests.
"It is never too late to do the right thing," he wrote in a Facebook post. "It is my considered opinion and stance that the results of the December 1st election represent a true reflection of the sovereign will of the Gambian people."
On Tuesday night Jammeh sacked his minister of youth and sport, a statement carried on national television said, without providing reasons for the dismissal.