The sacking is the latest controversial move made by Neuchatel's Chechen owner Bulat Chagaev, who has been the club's majority shareholder since May.
In that time he has now dispensed with the services of five coaches, with Didier Olle-Nicolle, Bernard Challandes, Sonny Anderson and Francois Ciccolini the other men to be dismissed.
L'Express report that Caparros' replacement will be another Spaniard, Victor Munoz.
Munoz, 54, enjoyed a successful playing career, featuring notably for Real Zaragoza, Barcelona and Spain.
His coaching experience includes spells at Villarreal, Zaragoza and Getafe, but he lasted a matter of weeks at the helm of Chechen club Terek Grozny earlier this year.
Chagaev's decision comes six days after he burst into the team's dressing room at the end of a 2-2 draw against Lausanne, terrorising the players and having to be physically restrained from assaulting Caparros by his own bodyguards.
In the wake of that incident, several Neuchatel players, who wished to remain anonymous, threatened to boycott the team's next match against Grasshopper, scheduled for September 11, if their salaries were not paid in full and if Caparros were sacked.