The Chilean forward continues to be linked with a possible future move away from the Emirates Stadium as negotiations regarding a new contract endure.
In the past, the Gunners have allowed a host of key players leave in their prime and former Liverpool midfielder Redknapp suggests it should be a priority of Arsene Wenger's to secure the services of Sanchez for the foreseeable future.
"It's imperative that Arsenal can convince him to sign a new deal before his current contract runs out in 2018," he told Sky Sports.
"It's not just about how much he brings to the team; tying him down would be a statement of intent and help the club to add more world-class talent.
"They'll find it very difficult to do so if they start losing their best players again, as occurred when Cesc Fabregas, Robin van Persie, Samir Nasri and Alex Song all left in the space of two seasons."