The Foxes have made an audacious attempt to sign the highly rated Portuguese forward after approaching Barcelona with an offer worth £45 million (€50 million), according to The Guardian's Fabrizio Romano.
The deal is somewhat unconventional, as it involves Leicester City signing him on loan for two seasons with an obligation to buy, Romano adds.
The 20-year-old was signed by Barcelona for £28 million (€31 million) in January, but it was agreed he would finish the season at Braga. He played his final game for the Portuguese club on July 27.
Trincao committed his future to the Catalan side until 2025 when he put pen to paper on a contract that also includes a €500-million buyout clause.
While Barcelona prefer to keep Trincao, they may be forced to sell out of desperation, as Romano reports the club is eager to raise funds by offloading some players due to financial restrictions caused by the coronavirus pandemic.
Atalanta have also been linked to Trincao, but the Italian club is not believed to be a serious contender, Romano adds.
Trincao, who has yet to receive a call-up to the Portuguese national team, had seven goals and eight assists in 27 league appearances last season at Braga.