Mendoza, who's now a Democratic State Representative, was among officials who announced their support for Cochran in his South Side campaign headquarters.
The alderman is a retired Chicago police officer who served for 26 years.
Cochran was elected to the City Council in 2007, and he is now running for re-election to a second term.
Cochran received 46 percent of the February 22 vote in a five candidate field. He is now facing a run-off with against rapper Che "Rhymefest" Smith.