De Jong will depart for Barcelona at the end of the season in a switch worth a potential €86m but Ajax have already moved to bring in a successor.
Romania international Marin will join on a five-year contract from Standard Liege but the 22-year-old says he should not be directly compared to De Jong.
"I want just to be me," Marin said to Ajax's website. "I saw that everyone compared me with Frenkie but I think we are two different styles of players because he plays more in front of the defence.
"He stays there, he has good quality of passes, he can eliminate [players] during the games. I'm more dynamic. I like to go into the opposition box, to score, to help my team with how I compete."
Ajax, two points behind PSV in the Eredivisie title race, face Juventus in the quarter-finals of the Champions League this month.