The battling midfielder was one of 11 first-team players released by the Saddlers, after Mat Sadler was confirmed as the club’s new head coach following his stint as interim boss.
Kinsella spent 19 years at Walsall, having joined the academy at eight years old, and went on to make 253 first-team appearances.
Following his release, the fan-favourite has now been linked to fellow League Two sides Swindon and Colchester.
Swindon will be led by former Walsall boss Michael Flynn next season, who was sacked in April by the Saddlers hierarchy, while Colchester are expected to have a healthy budget next season and could move for free agent Kinsella, who is expected to have several suitors across the Football League.
Meanwhile, work has begun on a new pitch at the Poundland Bescot Stadium.
Images released by the club show the old pitch being taken up, before a new surface is laid.
Walsall regularly use the off season to get their pitch ready ahead of the next campaign.