Dawson is out of contract at Glanford Park this summer, and is free to move wherever he likes.
SUFC will be able to demand a fee however, with a tribunal deciding the eventual fee if neccesary.
"Andy Dawson is a player we are aware of. We have been out to watch a number of games, especially of late," said Grimsby player-manager Paul Groves today.
"Whether he joins us is just speculation at the moment."