Both the Scunthorpe Telegraph and Grimsby Telegraph have linked the 37-year-old midfielder with a move to United until the end of the season.
He was sacked as manager of Grimsby on Monday, but remains a player with the club who saw their struggle at the bottom of Division Two worsened with a 6-0 drubbing at Oldham on Sunday.
Groves was a player under current Iron manager Brian Laws when he cut his managerial teeth with the Mariners in the mid-nineties, and Laws has made no secret of his need for an experienced midfielder to help avoid being sucked into an end of season relegation battle.