The midfielder's future has been the subject of much speculation this summer, with a number of clubs said to be competing to sign him from Leeds United following the club's relegation from the Premier League.
Chelsea were recently linked with the 24-year-old, but the Blues ultimately switched their attention to Moises Caicedo and Romeo Lavia, beating Liverpool to both players.
According to the Daily Mail, Bournemouth are now on the verge of signing Adams in a £20m deal, with the American passing his medical on Friday.
The report claims that the midfielder will pen a five-year contract with the Cherries.
Adams, who has also been linked with Brighton & Hove Albion of late, made 26 appearances for Leeds during the 2022-23 campaign following his arrival at Elland Road from RB Leipzig.
Elsewhere, Southampton are allegedly keen on Saarbrucken midfielder Luca Kerber.
The Saints are in the market for at least one new midfielder, potentially two, having allowed both James Ward-Prowse and Lavia to leave the club this summer.
According to the Daily Mail, Kerber has emerged as a genuine target, with the Championship club aiming to beat a number of teams to his signature before the end of the transfer window.
The 21-year-old came through the youth system at Saarbrucken, who play their football in the third tier in Germany.
Kerber has scored four goals and registered nine assists in 89 appearances for his current side.
Brondby are said to have recently failed with a £400,000 offer for the youngster, but there is a belief that a deal could be done for a fee in the region of
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