Ex-Brive, La Rochelle and Toulon coach Collazo took over the 2022 champions in November from Englishman Richard Cockerill on a two-year deal as disgraced former French Rugby Federation president Bernard Laporte was appointed director of rugby.
"We knew too well it was short term," Collazo told Sud Radio later.
"That's why I accepted the assignment from Montpellier," the 50-year-old added.
Montpellier, owned by outspoken Mohed Altrad, finished 13th in the league and needed to beat Grenoble in Sunday's relegation play-off to avoid dropping to the second division.
Altrad will hold a press conference on Tuesday to confirm the details with the club's former scrum-half Benoit Paillaugue in line to come into the coaching set-up.
Former New Zealand centre Benson Stanley is set to remain as defence coach.
Montpellier's squad includes two-time Rugby World Cup winner Cobus Reinach and ex-All Blacks winger George Bridge.
The southern outfit have been linked with former England forwards Mako and Billy Vunipola for next season.