Davies signed for the newly-promoted Potters from Southampton in the summer but has yet to make his bow due to a knee injury.
The former England Under-21 international underwent minor surgery last month and is now pushing for a place in Tony Pulis' side.
He told The Sentinel: "I have been training since the middle of last week and everything has felt fine.
"Hopefully, I will be able to play in the reserves and, if I get through that, I could maybe even push for a place in the squad for the Hull game.
"With two weeks' full training and 90 minutes of football under my belt, it is possible I could be involved."
Stoke, who currently lie 15th in the table, take on West Bromwich Albion this weekend before hosting the Tigers on 29 November.
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