The 32-year-old St Vincent international joined thae Latics last summer after spells with Rushden, Crewe and Torquay
Jack, free agent after being released by Oldham earlier in the year, made just 10 appearances at Boundary Park in a season blighted by injury.
Jack could replace Chris Llewellyn in the Wrexham squad with the 25-year-old Welsh international rumoured to be sold to Hartlepool this week.
Meanwhile, it is believed that Wrexham's top goalscorer Juan Ugarte is set to join Crewe Alexandra when he returns to the UK from Spain.