Adama Barrow is due to be inaugurated as the new president on Thursday, and West African military forces are poised to move in.
Mauritanian President Mohamed Ould Abdel Aziz met Mr Jammeh for last-minute talks before flying on to meet Senegal's President Macky Sall.
Mr Barrow won elections last month.
Senegalese troops remain stationed at the Gambian border, as the deadline for Mr Jammeh to stand down passed at midnight.
The threat of military action is supported by Nigeria and other states in the region.
