hello sri hari!!
there are no colleges that teach specifically  football management course in tamil nadu. however , In TAMIL NADU PHYSICAL EDUCATION AND  SPORTS UNIVERSITY you have a course -

P.G. Diploma in Sports Coaching (Athletics, Basketball, Football, Hockey and Volleyball) - eligibility -

Any Degree with three times Representation in Senior or Junior nationals / Inter University/Inter Services / Inter Department Tournaments (or) Any Degree and B.P.Ed / M.P.Ed., with two Times Representation in Senior or Junior Nationals / Inter University / Inter Services / Inter Department Tournaments.

please see : https://www.tnpesu.org/coursesoffered.html

hope this helps

thank you