The Portuguese was confirmed as AC Milan's new head coach on Tuesday, taking charge of a club that finished fifth in Serie A last season and will play Europa League football next term.
Reports throughout the season had suggested Milan were keen to sign a new central striker, with Paris Saint-Germain forward Goncalo Ramos among the names previously linked with a move.
According to La Gazzetta dello Sport, Ramos has now emerged as Amorim's dream signing as he looks to strengthen his attacking options at San Siro.
The Portuguese forward holds a contract with PSG that runs until the summer of 2028.
PSG are reported to be seeking a fee of around €40m to allow the 24-year-old to leave the French champions this summer.
Ramos scored six goals and provided one assist in 30 league appearances last season, starting 13 of those matches as he continued to operate largely as a squad option in Paris.
He has been more prolific on the international stage, scoring ten goals and providing three assists in 25 caps for Portugal's senior side.
Earlier in his career, Ramos came through the ranks at Benfica, where he scored 41 goals in 106 competitive appearances before his move to PSG.
Amorim's interest in Ramos is understood to stem partly from his time managing in Portugal, where he closely followed the forward's progress through the Primeira Liga before his transfer to France.
Securing a forward of Ramos' profile would represent a significant statement of intent from Milan as they look to rebuild following a disappointing campaign that ultimately cost Max Allegri his job.
Whether PSG would be willing to sanction a sale at Milan's preferred valuation remains to be seen, with the French club having invested heavily in Ramos since his arrival from Portugal and showing no urgency to lower their asking price.
Amorim's first transfer window in charge is expected to be shaped significantly by his familiarity with Portuguese football, with several other targets from his time at Sporting also reportedly under consideration as he assembles his squad for next season.
Milan's recruitment strategy under the new coach appears to be built around two parallel tracks, combining familiar faces from Amorim's Sporting days with proven performers from elsewhere in Europe capable of making an immediate impact.
Ramos would fall into the latter category, with his experience at the highest level of European football and his record for Portugal making him an appealing option regardless of his more limited role at club level last season.