The Cherries are light in the left-back area after Jordan Zemura and Matias Vina left the club at the end of last season.
Zemura signed for Udinese on a free transfer following the expiry of his contract, while Vina returned to Roma after spending the second half of the season on loan at Bournemouth.
There was a suggestion that Bournemouth would attempt to sign Vina on a permanent deal, but the Daily Echo has revealed that they have cooled their interest.
Instead, the South Coast club have stepped up their efforts to recruit Kerkez, who has been in talks with Italian side Lazio.
The defender had reportedly agreed personal terms with Lazio, but Bournemouth have swooped in to secure the Hungarian's signature.
According to journalist Fabrizio Romano, the Cherries have hijacked Lazio's bid and are now set to sign Kerkez after reaching an agreement with AZ Alkmaar over a deal worth a total of £15.5m.
The Hungary international is expected to fly to England on Tuesday, with a medical set to take place within the next 48 hours.
Should everything go according to plan, the player will put pen to paper on a long-term contract with the Premier League club.
Bournemouth were previously linked with a move for Kerkez during the January transfer window, but they decided against making a formal approach.
As a result, Kerkez remained in the Netherlands and helped AZ Alkmaar reach the Europa Conference League semi-finals, where they were beaten by eventual winners West Ham United.
The 19-year-old, who has earned eight caps for Hungary, is now set to leave AZ Alkmaar after making 57 appearances across all competitions.
Bournemouth have already signed Hamed Traore, Justin Kluivert and Romain Faivre this summer, although the latter has been immediately sent out on loan to French side Lorient.