The La Liga outfit's manager Vincenzo Montella has earmarked his attack as an area to strengthen ahead of next season and, according to Marca, the Portuguese forward is among his top targets.
However, the report suggests that Sevilla will only have the means to bankroll a move for Silva if they qualify for the Champions League.
English Championship outfit Wolverhampton Wanderers have also been linked with the Milan striker.
Meanwhile, Sevilla have been tipped to make Sandro Ramirez's loan move from Everton permanent at the end of the season, in a further attempt to boost their strikeforce.
Montella's side currently occupy fifth place in La Liga, eight points off the Champions League positions.