New York-based sports agent Ron Waxman also confirmed the deal, but both the club and MLS have denied that an agreement has been completed, according to ESPNFC.com.
The 32-year-old and Atletico Madrid lost the Champions League final to Real Madrid on Saturday, but helped Atletico to a La Liga title this season.
Villa signed with Atletico Madrid last summer after a three-year stint with Barcelona and five seasons with Valencia.
He has scored 56 goals in 94 appearances for the Spanish national team and was part of the 2010 World Cup-winning team.
NYCFC is not scheduled to begin play until March 2015. SI WIRE: Real Madrid punished by UEFA for fans’ racist behavior