The 22-year-old, better known as Gabigol, joined the Nerazzurri in the summer of 2016 for just under €30 million, but found first team chances limited and loan spells with Benfica and Santos followed.
With his imminent return to Inter this January, Sportmediaset understands cross-town rivals Milan are considering making an offer for the Brazilian, with sporting director Leonardo leading the pursuit.
West Ham United appear to be favourites to land Gabigol in January, and are viewed as a more favourable destination by the Nerazzurri.
However, were the Hammers to turn their attention elsewhere then both Milanese sides could come to the negotiation table, providing the Rossoneri a chance to buy Gabigol permanently.
The two sides have had dealings in the past despite their rivalry, the last of which came in 2012 when Antonio Cassano and Giampaolo Pazzini moved in opposite directions.