One described how a plane rented from Damojh airlines had completely dropped off radar systems around eight years ago, while another alleged poor maintenance.
Mexican authorities say they will carry out a safety audit of the company, BBC News reports.
Three women survived the crash near Havana airport - Cuba’s deadliest air disaster in more than 30 years.
Cuban authorities have launched an investigation into the accident, as rescue workers continue to comb through the wreckage site around 20km (12 miles) south of Havana.
One of two the aircraft’s black boxes has been recovered and is said to be in good condition.
