Baxter, 17, from Bootle in Merseyside, and two other men, aged 29 and 34, were arrested in the Kirkby area on Monday.
A spokesman for Merseyside Police said: "Three men have been arrested in Kirkby on suspicion of possession of cannabis with intent to supply and possession of counterfeit money.
"All three men have been released on police bail pending further inquiries."
A spokesman for Everton Football Club refused to comment.
Centre-forward Baxter made his professional debut for the club on the first day of last season as a substitute.
The appearance made him Everton's youngest ever senior player, aged 16 years and 191 days.
This season he has represented the team twice in the Europa League.