Carter has also been linked with Fulham and Scottish giants Rangers.
Carter will spend the next few weeks on trial with Villa.
“I first saw Jordon in the trials this summer and I thought he was fantastic,” said Town boss Steve King.
“He has been training with the first team since then, and he scored a hat-trick on his debut for the U18s, despite giving away nearly three years to most of the opposition.
“It is good to see that others are now beginning to recognise his talent. There has been a lot of interest from a number of Premier League clubs and one big club in Scotland as well.
“But Aston Villa are a club with a great reputation for bringing through young English talent, and it’s a great opportunity for Jordan.”