The island club are seeking a new coach after axing Jagoba Arrasate this week.
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Radio Marca says Demichelis is now in advanced talks about taking on the post to the end of the season. Mallorca currently sit third from bottom on the LaLiga table.
For his part, Demichelis has accepted the short-term proposal, with no guarantees he will be kept on next season even if Mallorca beat the drop.
Demichelis has in the past taken charge of River Plate and Monterrey.