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French media outlet Midi Libre is reporting Foster, whose four-year term as head coach of the All Blacks expired at the end of this year's World Cup, and Schmidt, who has also previously coach Ireland, could be called in to rescue the Top 14 club side.
Montpellier have won just one of the seven matches this season and sacked head coach and former England international Richard Cockerill at the weekend.
Cockerill's dismissal came after former France coach Bernard Laporte was recently appointed Montpellier's director of rugby last week.
Laporte has brought in Patrice Collazo from Brive but only on an 18-month contract with Midi Libre reporting both Foster and Schmidt are being lined up as potential head coach candidates in the long run, with Schmidt reportedly being the priority.
Scott Robertson is the new coach of the All Blacks.