And he says the club must 'respect' the brilliant Belgian's decision to quit Stamford Bridge as they prepare to face Arsenal in the final in Baku on May 29.
Hazard, 28, has made his desire to leave Chelsea for Real Madrid clear having refused a new contract offer.
A deal between the two clubs is yet to be finalised for the forward to leave London, with Azpilicueta holding no ill will over his team-mate's readiness to move on.
"He is a very important player for us," he told Sky Sports. "We arrived [at Chelsea] at the same time and, obviously, we want him to stay with us but we have to respect his decision.
"His mind is only on doing well with Chelsea and lifting the trophy in Baku. Then we will see."
Chelsea have travelled to Boston for a charity friendly with New England Revolution ahead of the final.
But Azpilicueta says the trip will not adversely affect preparations for meeting the Gunners in Azerbaijan.
"We have to do anything - train hard, to rest - we have nearly two weeks until the final so it's very important to arrive in the best condition for the final," he added.
"Hopefully we can get in a good shape and lift the trophy."
Chelsea could look to Barcelona to replace Hazard with the Catalan club's hierarchy bracing themselves for interest in Philippe Coutinho.
Goal understands that even though Coutinho wants to remain at Camp Nou, some members of the club's board of directors are keen to sell this summer following a disappointing first full campaign from the Brazilian.
The Londoners would seek a replacement for their influential forward should their FIFA-inflicted transfer ban be delayed by the Court of Arbitration for Sport (CAS).
It is understood that a decision on the two-window long suspension for registering senior players will be made before the closure of the upcoming transfer window.
Hazard scored 16 goals and made 15 assists in the Premier League in 2018-19.