The Malian government has begun talks with local leaders in the north of the country aimed at freeing the tourists, who were seized more than four months ago in the neighbouring Algerian part of the Sahara desert, official Malian sources said.
Separate German government-approved negotiations were underway elsewhere, the source added.
The kidnapped tourists - nine Germans, four Swiss and one Dutchman - are believed to have been abducted by the Salafist Group for Preaching and Combat (GSPC), a radical Islamic group with alleged links to al-Qaeda.
They went missing in February and March while travelling without local guides in Algeria's vast desert, where temperatures at this time of year climb as high as 50 degrees Celsius.
Death in the Sahara
A 15th hostage, 45-year-old Michaela Spitzer from Germany, died about two weeks ago of heatstroke, according to German and Algerian sources quoted in media reports this week.
Unidentified bounty hunters have reportedly been approaching the kidnappers, thought to be hiding out in the northeastern Kidal region, and offering to buy the Europeans and bring them back to the capital Bamako where they would expect a reward.
"If the hostages are still alive, then our German friends are going to have to accept that we will coordinate negotiations, because we are running out of time."
The kidnappers are annoyed by the number of people approaching them seeking the hostages' release, according to the official source in Bamako.
"(The kidnappers) clearly stated their annoyance at the number of mediations," and repeated their desire that, for their own safety, they should not go back to Algeria, he said.
Meanwhile, Malian negotiators said that they had met two of the kidnappers, in Mali, in the middle of the week, without saying how many kidnappers there were in all, according to the same source.
The German-approved negotiators are believed to have been given two off-road vehicles by the Malian authorities and headed off to the northern region where foreign media have reported the kidnapped tourists to be located.
The Malian official added that the number of negotiations underway was creating a very confusing situation in the north, "with all sorts of contradictory information emerging", he said.
"If the hostages are still alive, then our German friends are going to have to accept that we will coordinate negotiations, because we are running out of time," he continued.
Malian authorities on Friday said they had received a video cassette of the tourists in which they appear to be in good health and which appears to confirm a ransom demand made by their abductors.
While no ransom figure was mentioned in the video, Germany's N-TV television reported that a suspected Islamic group was demanding 4.6 million euros ($5.2 million) for each hostage.
Berlin's close ties to Mali have raised hopes that a deal may be struck soon to release the travellers.
Seventeen other European tourists abducted in similar circumstances in the same area were freed in a raid by Algerian special forces in May.