The 22-year-old is said to have decided against a new deal, with a year left on his Benfica contract, raising the prospect of a Lisbon exit.
Reports in Europe say the clubs are in advanced talks and closing in on a deal, and the Daily Echo understands discussions are well under way.
Silva has made 181 appearances for the Portuguese giants, scoring ten goals and providing four assists.
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He progressed through the club’s academy after he joined the club in 2016, and made his first team debut aged 18 in August 2022 and helped Benfica to a clean sheet and a 3-0 win over Boavista.
The centre-back became a first-team regular that season, playing 44 times in all competitions, including all 10 Champions League games as Benfica reached the quarter-finals.
In subsequent seasons, Silva made 50 and 46 appearances in all competitions for Benfica, before playing 41 times last season for the Portuguese top flight side.
He has also played for the Portugal age-group sides from U16 to U21, and has 20 caps for the senior side after making his debut aged 19.
Bournemouth are prioritising a new centre-back after the departure of Marcos Senesi at the end of his contract last season.