Inter's interest was first reported by Brazil-based outlet GE.
Inter has money to spend after concluding the transfer of Yuri Alberto to Zenit St. Petersburg for $22 million, though one source cautioned that negotiations are in the early stages. Inter recently acquired Aston Villa attacker Wesley Moraes after he cut short his loan with Club Brugge.
River Plate has also shown interest, and Castellanos has spoken of his dream to one day play for the Argentine giants.
River's plan is to sign Castellanos for the start of the 2022 Copa Libertadores, which begins in April.
Sources have told ESPN that would like to receive between $15m to $20m on a deal.
Brazilian Serie A side Palmeiras made an offer of about $12.5m, which the MLS team rejected, though sources have told ESPN that the Verdao remain interested in the striker.
Brazil's transfer window closes on April 12, while Argentina's will conclude on Feb.19.
A native of Mendoza, Argentina, Castellanos originally joined NYCFC on loan in 2018 from Uruguayan side Montevideo City Torque, another City Football Group club. He made the move permanent at the conclusion of that season.
In 35 league and playoff appearances in 2021, Castellanos scored 22 goals and added eight assists while winning the Golden Boot. He also scored in the MLS Cup final triumph over the Portland Timbers. In parts of four seasons with NYCFC, he scored 40 goals with 18 assists in 99 league and playoff appearances.
ESPN's Javier Nievas contributed to this report.