The deal included him going into exile in Mauritania.
He later had a change of heart and said he will only go into exile if judges at the Supreme Court rule against his petition in May.
A disappointed President Aziz left Banjul late in the night for Senegal where he held talks with President Mack Sall.
Mr Jammeh’s mandate expired at midnight after his surprised defeat in last month’s election by opposition candidate Adama Barrow.
He had vowed to cling to power after accusing the country’s electoral commission of rigging the election in favour of the opposition.
His attempt to overturn the election result at the Supreme Court has been delayed because of a shortage of judges as most of the judges come from neighbouring countries
Mr Jammeh’s refusal to step down has open the door to a Senegal led military intervention to installed Mr Barrow.
Meanwhile, as Senegalese and other troops massed on the Gambia’s borders, the country’s Chief of Defence Staff, Ousman Bargie, said he would not order his men to fight other African troops if they enter into the country.
“We are not going to involve ourselves militarily. This is a political dispute,” he said, after eating dinner in a tourist district close to the capital, Banjul, eyewitnesses told AFP.
“I am not going to involve my soldiers in a stupid fight. I love my men,” he added, stopping to pose for selfies with admirers while dressed in fatigues, beret and green t-shirt, according to those present.
Meanwhile at the time of writing this report, a Senegalese radio station is reporting that Senegalese soldiers have crossed into Gambian territory. The reporter said the heavily armed soldiers are entering the Gambia via land and sea.
The Nigeria Airforce, which is already in Dakar, is on standby and would be deployed to help neutralise any resistance.