Grant has impressed since leaving Derby County for Stoke City on loan.
Aston Villa reportedly have their eyes on two goalkeepers.
Molde and Norway goalkeeper Orjan Nyland is reportedly wanted by up to 15 clubs, including Newcastle United and Celtic.
The 24-year-old stopper has long been tracked by Everton, but Southampton are prepared to match his buy-out clause.
Manchester United have reportedly told Ben Amos he can leave, while Anders Lindegaard could be swapped for Norwegian international Ørjan Nyland
Manchester United could be set to swap Anders Lindegaard for Orjan Nyland in January.
Arsenal have been scouting young goalkeeper Orjan Nyland for the past 18 months according to reports.
All the latest news and gossip from The Emirates this evening.