As well as Middlesbrough and Derby County, Aston Villa have been credited with interest in Odegaard, who it is claimed could leave Real Madrid on loan this month.
Stoke are yet to be linked with the Norwegian teenager, but it is they who lead the betting - ahead of Middlesbrough (5/1), Derby (6/1), Swansea City (7/1), Nottingham Forest (8/1) and Leeds United (9/1).
Odegaard - who at the age of 19 already has 12 caps for his country's senior team - spent most of last season playing right wing for Heerenveen in Holland's Eredivisie, but can also operate in a central attacking midfield role.
And while Stoke are not currently short in either of those positions, speculation continues to link Badou Ndiaye, Mame Biram Diouf and Eric Maxim Choupo-Moting with moves away from the Bet365 Stadium.
Aston Villa, Middlesbrough and Derby are among those tipped to challenge pre-season favourites Stoke for the Championship title this season.
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