The former West Ham and Blackburn striker has been training with the Parow-based side for the past week in a bid to get fit.
But Carelse says the new-look player is keen to don the red and white of Ajax next season as they look to avenge last season's last-day heartbreak.
The former SuperSport United player also revealed Benni would be willing to take a pay cut to sign for the club.
Carelse told the Citizen: "He told me he is here to stay."
With regards to McCarthy's potential high wages, Carelse added: "This is something he also cleared with me.
"He said money was not his driving force and that he has made enough of it through the game."
McCarthy left West Ham after being paid out of his long-term contract. His much-publicised weight problems saw him struggle for game time at the Hammers but he looked slimmer and sharper at Ajax training.