The Definition of Done is under the Scrum Team's control, either being derived from an organizational standard or created by the Scrum Team for the product being developed. If the Definition of Done comes from the organization, it becomes a minimum standard for the Scrum Team to follow and may be made more stringent.
The Scrum Guide, as of the November 2020 revision, doesn't provide any guidance as to what must be in the Definition of Done, leaving it entirely up to the Scrum Team. Therefore, the Scrum Team could state that a Product Backlog Item does not meet the Definition of Done until it has been appropriately reviewed and approved by the Product Owner. Just because it's permitted, however, doesn't mean that it's a good idea.
If either the Product Owner or the Developers feel that approval is necessary as part of the Definition of Done, I suspect that there are larger issues to be resolved. Once a Product Backlog Item is selected for a Sprint and included in the Sprint Backlog, the Developers should be able to get that work Done on their own. After all, the Scrum Guide does say that Developers "are committed to creating any aspect of a usable Increment each Sprint" and an Increment is not created until a Product Backlog Item meets the Definition of Done. There's no reason for anyone outside of the Developers to be involved in meeting the Definition of Done.