Forest swooped to sign two Benfica players last week, buying Joao Carvalho and loaning Diogo Goncalves.
Paciencia spent last season on loan at Vitoria Setubal, where he scored 10 goals.
There is also reportedly interest from Italian, Spanish, and German clubs.
The report claims Porto will consider offers starting at seven million Euros - £6.1 million.
Paciencia earned a call up to Portugal's international team last November, making his debut in a friendly against USA.
He has made 16 first team appearances for Porto so far in his career.
He is a player known to Nottingham Forest owner Evangelos Marinakis, as Paciencia had a brief stint on loan in 2016/17 at his Olympiakos side.
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