Davis scored in Villa's 4-0 win at Burton Albion earlier this week, to continue an impressive breakout campaign for the former non-league teenager.
But a report on the Birmingham Mail's website on Thursday suggests that a different Aston Villa player, Jonathan Kodjia, was the focus of Everton's attention - be it in addition to or instead of Davis.
Everton were linked with a move for the Ivorian towards the end of last season, in which he scored 19 goals from 40 Championship appearances.
But an ankle injury kept Kodjia sidelined throughout the summer transfer window, and appears to have worked in Villa's favour if Everton have indeed returned to the scene almost immediately after his return to fitness.
Could he be the man to replace Romelu Lukaku in January?