According to the NFL rules, a coordinator position is considered a lateral move from a positions coach (like LB, DB).
If we wanted to interview to replace CSP, then the current club is required to grant permission, but not for this.
The NFL does not differentiate between levels of assistant coaches in its rules regarding their availability to interview with other teams. Whether the coach is a defensive line coach or an offensive coordinator, the rules are the same. If a team wishes to interview an assistant coach who is still under contract with another team for its head coaching position, the current team is required to give permission for the interview as long as it happens between the end of the team's season and March 1. After March 1, teams can still ask, but the current team is not obligated to give permission.
An NFL team cannot interview an assistant coach who is under contract as an assistant with another team for the following season without the permission of his current organization. Teams will usually give permission upon request, particularly if a lower level coach is set to take an offensive or defensive coordinator position elsewhere, but the current team is not required to give permission.