The Welsh winger is currently in his third month on-loan at Blundell Park this term, and Mariners chief Groves admits he would like to retain Oster's services on a permanent basis.
The 24-year-old, who made his name at Grimsby, left the club for Everton in a £1.5 million deal in 1997.
After failing to establish himself on Merseyside though, the midfielder moved on to Sunderland.
Despite the Wearsiders' desperate plight this term, Oster has not managed to force his way into Howard Wilkinson's plans and Grimsby are now ready to try and lure the diminutive wide-man back to Humberside in a £75,000 deal.
"I would like to keep him here, and the fans want me to keep him here," stated Groves.
