Mexico coach Lozano sacked after Copa América disappointment
Lozano had been offered the chance to continue as an assistant until the 2026 World Cup before returning to the role of head coach until 2030 but he rejected the proposal, FMF added.
Mexico will co-host the 2026 World Cup with Canada and the United States.
"Following the Copa América, the FMF has begun an analysis to determine mistakes, and successes and evaluate areas for improvement in the process," it said in a statement.
"Jaime Lozano was offered a contract until 2030 in which, during the period 2024-2026, he will accompany a more experienced manager towards our World Cup.
"Lozano has informed us that he does not wish to continue. We respect his decision, we recognise his great professionalism, capacity and dedication."
Lozano, who spent just one year in the job, led Mexico to the 2023 Gold Cup title and reached the CONCACAF Nations League final earlier this year, losing to the United States.
The former Mexico international posted 10 wins, four draws and seven defeats during his time in charge.
Reports in local media say Javier Aguirre will replace Lozano as Mexico manager for his third stint having coached the side at the 2002 and 2010 World Cups.