But Alexander, who has only just returned to management after recovering from a brain tumour, has denied that he is interested in the position.
He said: "it's laughable how these things come out, I've not been approached by Grimsby.
"I've got enough on my plate here to worry about what's going on up there. We've got a big month coming up in the league and all my attentions are on that."
Imps chairman Rob Bradley expects Alexander, who was at Grimsby as a player, to sign a new contract to stay at the Imps.