Cardinal Philippe Barbarin, archbishop of Lyon, recently told journalists that the monks want to return to the Monastery of Our Lady of Atlas, about 100 kilometers (62 miles) south of Algiers.
The cardinal went on a pilgrimage to Algeria with Azzedine Gaci, the president of the Rhone-Alps Muslim Council.
The interreligious pilgrimage included a stop at the now-abandoned monastery, where both men led prayers and called for dialogue. The cardinal especially asked prayers for the planned return of the Trappists, since previous attempts have failed.
Just two years after the killing, four monks expressed the desire to reopen the monastery. However, no precise date was set and the Algerian minister of the interior warned against the monks' return for security reasons.
However, the four monks -- from Algeria, France, Spain and Poland -- stayed in Algiers to learn Arabic and French.
Algeria is a Sunni Muslim state. Christians and Jews account for only 1% of the country's 32 million people. There are about 23,250 Catholics in Algeria, 136 priests and 210 women religious.