The experienced stopper has fallen out of favour at the KC Stadium after a rumoured dressing room bust up with Peter Taylor.
Fettis has spent time on loan with Sheffield United this season to ease their goalkeeping crisis. His first spell with Hull in the early 90's saw him become a folk hero when he came off the bench, as a striker, to score on two occasions.
Since then he's had big money moves to Blackburn and Nottm Forest.
Anderson, a dominating centreback, is highly rated by the Hull fans but has failed to recover from injury in recent months and has failed to make a first team apperance this season.
The Scot has earned rave reviews since his switch from Livingstone and was the Tigers player of the season last year.
Anderson is free to leave the KC and has already this week rejected a move to Boston United. The Pilgrims in turn signed Anderson's Hull team-mate Greg Strong, a one time Alan Buckley target for Town.
"We need to stiffen it up at the centre of our team," Law told the Grimsby Telegraph.
"Obviously I have made a lot of phone calls and asked a lot of people about a lot of players and John Anderson has come into the equation given the situation we are in on short-term deals.
"We'll have to see if anything comes of that in the next few days."