The former Barcelona attacker has revived his career at Sporting, where he played for Ruben Amorim before the latter left for United late, last year.
A Bola says United and City, where former Sporting technical director Hugo Viana is succeeding Txiki Begiristain this summer, are both keen.
Trincao has a deal at Sporting to 2026, with his contract carrying an €80m buyout clause.
Barcelona are also watching developments, as they hold a 50 per cent sell-on clause on Trincao, who has previous experience in England with Fulham.