Saunders made just three appearances for Pools while on loan from Fleetwood Town before his season was effectively cut short by a knee injury picked up last month.
The 23-year-old was named as one of the players who wouldn’t be offered a new deal at Fleetwood when their retained list was published, making him available on a free this summer.
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Barton signed Saunders for Fleetwood from Darlington in January 2019 before he was loaned straight back to Pools’ local rivals.
He joined Dave Challinor’s side on loan in April 2021, making his debut off the bench in the 3-1 win over Chesterfield before starting the defeats against Bromley and Maidenhead.