De Jong will join the Catalan outfit next season in a deal reportedly worth €75 million after signing a pre-contract last month.
Bartomeu has now confirmed De Jong's club and international teammate, Matthijs de Ligt is being considered as a possible target.
“This is a player who would be under consideration,” Bartomeu told Ser Catalunya, according to Marca.
“We are always looking at the best players and those talents will always interest Barcelona, so he will be a name in our plans for sports planning.
“We moved quickly for Frenkie de Jong because other clubs had approached him.”
Both de Ligt and De Jong played starring roles as Ajax eliminated Barca's rivals Real Madrid in the UEFA Champions League round of 16.