Pecker is a key witness in the case against the former US president, who is accused of falsifying business records to cover up hush-money payment
City are reported to have negotiated a £40 million fee with relegated Bournemouth, with the deal potentially rising by a further £1 million depending on clauses.
Ake's likely arrival at the Etihad Stadium comes after City endured a poor season defensively following the departure of Vincent Kompany to Anderlecht last year.
Hampered by a long-term injury to Aymeric Laporte and the disappointing form of John Stones and Nicolas Otamendi, City boss Pep Guardiola was forced to deploy Brazilian midfielder Fernandinho at centre-back.
City never looked settled at the back and that weakness played a key role in Liverpool ending their two-year reign as Premier League champions.
Ake had been one of Bournemouth's best players since joining from Chelsea in 2017.
There was expected to be strong interest in the 25-year-old during the summer transfer window and City have made their move now in a bid to secure his signature.
Ake, capped 13 times by the Netherlands, missed Bournemouth's final three Premier League fixtures after suffering a groin injury in 4-1 win over Leicester on July 12.
In his absence, Eddie Howe's side slipped into the Championship after five years in the Premier League.
Asked if Ake may have made his final appearance for Bournemouth after the Leicester game, Howe replied: "I think it would be silly of me to comment on that, to be honest, at this moment in time.
"I think next season and everything beyond it will take care of itself."
City are also reported to be involved in advanced negotiations with Valencia for the signing of 20-year-old winger Ferran Torres.
It is understand the Premier League side have agreed an initial fee of £20.9 million with Valencia and talks over potential add-ons are continuing.
City are in the market for a new winger following the departure of Leroy Sane to Bayern Munich.
Pecker is a key witness in the case against the former US president, who is accused of falsifying business records to cover up hush-money payment
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