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27-year-old Tonkin was released last summer from Crewe and rejoined Yeovil who he started his career with back in 1999.
Tonkin was released at the end of last season in which he found a place in the team very hard to come by and was loaned out to Grays Athletic.
Lincoln City manager John Schofield has beaten off interest from a few League Two teams as he looks to strengthen the Sincil Bank outfit.
If Tonkin was to impress he would link up again with former Crewe player Adie Moses.