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Jennings, 35, spent last season in the National League with Barrow, and previously spent time at Cantilever Park on loan in 2017/18.
He made more than 250 appearances for Tranmere in three spells, as well as playing for Coventry City, Motherwell and Southport.
A Scottish Cup finalist in 2011, Jennings has featured for the Yellows in pre-season against Accrington Stanley and Wythenshawe Town.
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