The Chile international was detained when police stopped an Audi Q7 in the south coast resort on Saturday morning, and he missed Brighton's home game with Burnley because he was in police custody. Reyes has been charged with driving while disqualified and driving without insurance and bailed to appear before Brighton magistrates on January 20.
Hodgson, who confirmed Reyes will be part of his squad at St James Park, said: "Gonzo is a very keen and enthusiastic footballer with plenty of energy in his game the way he plays.
"I'd be pretty surprised if he was to take it on to the field with him. Most footballers have got something else going on in their lives that they have to deal with when they go on to the football field and put it into another compartment.
"His is perhaps a bit more serious than others who have baggage to take onto the field. He'll have to learn to deal with it."