Sources close to mediators negotiating their release said the four were very ill and that their immediate release was a necessity.
“It is urgent for us that they are released on humanitarian grounds,” the French news-agency AFP quoted the source as saying.
Altogether, 14 hostages from Germany, the Netherlands and Switzerland are being held by members of a rebel Islamic group.
The Salafist Group for Preaching and Combat (GSPC) is said to have seized 32 tourists trekking without guides in the southern Algerian desert in February and March this year.
While 17 of the kidnapped tourists were freed in a raid by Algerian special forces in May, one German hostage died last month of heatstroke in the blazing sun.
'It is urgent for us that they are released on humanitarian grounds'
Mediators have been negotiating the release of the 14 remaining hostages with the kidnappers without much success.
The abductors are reportedly demanding about 5.5 million dollars in ransom for the release of each of the captives.
But with a breakthrough still elusive, local newspapers said a military intervention is being planned to rescue the hostages.
The kidnappers crossed the southern border into Mali and have been negotiating the release of their captives with local power brokers including former rebel leader Iyad Ag Ghali.
“If by Thursday or Friday at the latest there is no release of the sick hostages or the elderly, contact with the abductors will be halted to allow the military to take up the case,” the police commissioner of the northern Mali town of Kidal told the daily El Watan.