Vela, 21, has found opportunities limited this season with Arsenal predominantly playing with a lone striker, and Wenger has decided to allow him to move on loan to gain further first-team opportunities in the second half of the season.
"Bolton is one of the clubs that has shown an interest," Wenger said. "We have many clubs that have shown interest and I am not surprised.
"I want Carlos to play at the top, top level and the club who gives me the biggest guarantee to play will have the chance to sign him. I would expect it to happen in early January because he is keen to play.
"He has been patient and worked very hard - he has matured a lot and changed a lot in a positive way and is a fantastic boy who deserves to play.
"He is a fantastic talent and I do not want to lose him and I want him now to get experience."
Jack Wilshere spent the second half of last season on loan at Bolton and has since become a regular in the Arsenal first-team.