Asensio's representative, Horacio Gaggioli, acknowledged his client would be proud to hear of an offer from the Serie A club but says the 22-year-old wants to stay at the Santiago Bernabeu.
"It's an honour if a club like Inter are interested in Marco," he told FCInternews.
"I don't know if it's true, but for now the player has no intention of leaving Madrid."
Asensio has won eight major trophies for Madrid since 2016, including the 2018 Club World Cup this month.
Otro título para vosotros, Madridistas. ¡Tricampeones del mundo! / Another cup for us, Madridistas. World Tri-champions! pic.twitter.com/8PJSFYWGRI— Marco Asensio (@marcoasensio10) December 22, 2018