The 22-year-old has made just four Premier League appearances this season and has yet to start a game in the league for Villa.
He is distinctly down the pecking order of strikers at Villa Park and several clubs in the Championship are interested in Davis.
It has been claimed Stoke are one of the second-tier sides who have shown an interest in Davis and they are keen to take him to the bet365 Stadium this month.
Stoke are eighth in the Championship table and want to sign Davis on loan to boost their chances of pushing for promotion back to the Premier League.
But Aston Villa are unlikely to entertain any loan offers for the 22-year-old as Smith is still short of options in attack.
The striker is the only back-up option to Ollie Watkins for the Aston Villa boss has at the moment.
With Brazilian forward Wesley still out injured, Smith may not be interested in loaning out Davis this month.
It remains to be seen whether that stance changes if Aston Villa manage to bring in a striker in the ongoing transfer window.
