Senegalese troops have been seen moving towards the Gambian border in a show of force to pressure President Yahya Jammeh to stand down.
Senegal gave him a midnight GMT deadline to quit and Nigeria has sent an air force contingent to Senegal in support of the possible intervention.
Wednesday was meant to be his last day in office but parliament has granted him three more months in the post.
It effectively stops successor Adama Barrow being sworn in on Thursday.
His shock victory in the 1 December election plunged The Gambia into crisis. Mr Barrow is currently in Senegal.
West African countries are seeking UN backing to intervene militarily to eject Mr Jammeh, who has ruled The Gambia since taking power in a bloodless coup in 1994.
Meanwhile, thousands of UK and Dutch tourists are being evacuated from the tiny West African state, which is popular with European holidaymakers because of its beaches.
Ecowas, the Economic Community of West African States, has mandated Senegal, which almost surrounds The Gambia, to spearhead military intervention, but only as a last resort and with the backing of the UN Security Council.
“We are ready and are awaiting the deadline at midnight,” Col Abdou Ndiaye, a spokesman for the Senegalese military, was quoted as saying by Reuters news agency.
“If no political solution is found, we will step in.”
The Gambia’s entire armed forces are made up of only about 2,500 troops, making it difficult to see how they can defeat a regional force if it moves in, says BBC Africa Monitoring security correspondent Tomi Oladipo.
Nigeria says it sent fighters and other aircraft, along with 200 personnel, to Senegal on Wednesday morning.
Nigerian navy vessels are also on standby and a warship that sailed from Lagos on Tuesday will have the task of evacuating Nigerian citizens while putting on a show of force.
Ground troops are also being provided by Ghana.
Ecowas has always maintained that it will only deploy troops as a last resort, triggered by the overt use of violence by Gambian security forces against civilians.
A military operation by West African forces would first have to be approved by the UN Security Council.