Italian Di Canio left the County Ground earlier this week following a disagreement with the club's board.
A number of bosses have been linked with the vacancy, but Hockaday was thought to be one of the frontrunners.
However, the 55-year-old has insisted that he is extremely happy in his current job.
"I haven't been approached. I'm employed by Forest Green Rovers and I love my job," he told BBC Radio Gloucestershire. "I've got the best chairman in the world so I'm not going to go looking for another job.
"I'm Forest Green through and through. If ever my chairman wants me to leave then that's a different matter but until such time I'm happy here."
Hockaday made over 300 appearances for Swindon as a player during a seven-year stint with the club that came to an end in 1990.