The 33-year-old, who has scored twice and registered nine assists in 32 appearances for Gennaro Gattuso's side this season, will see his current deal in Naples expire at the end of June.
According to Eurocalciomercato, Villa are readying a three-year contract for the experienced forward as they attempt to beat Spanish duo Sevilla and Valencia to his signature.
The report claims that Callejon is also likely to have offers from the MLS and China.
The five-time Spain international joined Napoli from Real Madrid in the summer of 2013 and has scored 80 times in 336 outings for the Italian giants in all competitions.
Villa are currently 19th in the Premier League table, two points from the safety of 17th position with a game in hand over the rest of the teams around them. body check tags ::