Cleethorpes-born Darren Wrack has expressed a desire to return back to his native area. Both City and Grimsby are interested in bringing the Walsall midfielder back home. However, his wage demands could be a stumbling block for both clubs.
Tigers manager Peter Taylor has also confirmed his interest in Grimsby captain John McDermott.
He said: "John is another player I am interested in, but at this stage nothing has been signed.
"We don't want to rush into making too many signings until we know everyone who is out there and who is available."
Meanwhile, Taylor will be having talks with members of his squad regarding their futures. Elsewhere, ex-Tiger Mike Edwards has been released by Colchester.