The 24-year-old has been with the club for two seasons on loan, and they must now decide whether to secure him permanently.
Despite the team's lack of quality in central midfield, Wright does not believe Ceballos has merited a long term deal with the Gunners.
He would rather the club give Newcastle United loanee Joe Willock a chance to stack a claim for a first team spot next term.
Wright told Premier League Productions: "You say who's vulnerable, you look at [Lucas] Torreira and [Matteo] Guendouzi, Joe Willock is doing very well at Newcastle, [William] Saliba's doing well as well.
"You look at it and you think to yourself those players, every one of them apart from [Konstantinos] Mavropanos who's not really had a chance [and] Saliba, maybe those players should be where they are.
"I'd like to see Joe Willock get an opportunity but I don't think it's going to happen.
"I don't think we should be signing Ceballos, I just don't think he's what we need now.
"I think that we've got young players coming through who should get an opportunity in front of Ceballos.
"If he's going to do anything to stay at Arsenal it would've been seen already by now.
"[Martin] Odegaard is somebody who I'd like to see sign, but at the same time the people who are going to oversee who's coming in and who's going out are unfortunately the same people who signed someone like Willian for three years.
"Are we going to give those people the power to try to do this overhaul? I don't trust them. It worries me.
"As much as the manager is passionate and the players are working hard, I'm not sure I trust the people in charge to try and make stuff happen in the summer, to oversee that job. I don't see them doing it."