Their release would end the nine-month kidnapping saga, which has become the longest such incident to take place in the Sahara desert.
The Spanish newspaper El Pais reported that the two workers were travelling from their last hiding spot in the desert of Mali to the border of Burkina Faso, where Spanish government representatives were expected to pick them up.
A Malian security source told the AFP news agency that the pair were expected to
arrive at the border "at any moment".
"They're expected at the border at any moment and the operation in place is that a helicopter will collect them," the unnamed source said, adding the helicopter would fly the two men to the Burkinabe capital Ouagadougou.
Accio Solidaria, the charity the two men work for, said on Monday that they were waiting for official confirmation of their release.
"We hope that during the course of the morning this bit of news will turn out to be positive," Francesc Osan, head of the aid group, told Spanish radio RNE.
The reported development comes after Mauritania repatriated to Mali the man convicted of masterminding the kidnapping.
Al Arabiya television said on Sunday that the release of the hostages was linked to the return of Omar Sid'Ahmed Ould Hamma, who was jailed for 12 years by a Mauritanian court.
But officials in Mauritania and Mali have not confirmed whether the two events are linked.
AQIM has said that Spain is one of its targets because it is an ally of the United States and part of the Nato military alliance.