The Spaniard led Levante into 10th place in La Liga last term and had reportedly been close to signing a new two-year deal with the Granotes.
However, it has been revealed that contract negotiations between the two parties have broken down.
"We regret that, despite our efforts to reach an agreement, we have not been able to come up with a solution," read the statement.
"Levante would like to thank Joaquin Caparros and his coaching staff for their professionalism, hard work and dedication during the 2013-14 season."
A number of top-flight Spanish clubs are currently without a permanent manager.