Chelsea qualify automatically for next year’s Champions League as a result, but it remains unclear whether Hazard will be at the club for the 2019-20 campaign.
“[Hazard] has been an important part of the club for the last seven years,” Azpilicueta said after the game at the King Power Stadium.
“Everyone here loves him and we would like him to stay with us.”
Earlier this week Hazard secured a clean sweep at Chelsea’s end-of-season awards, picking up the Fans' Player of the Year, the Players' Player of the Year and Goal of the Season.
The No. 10 has contributed 19 goals and assisted 16 in 51 games for the West London side this year, and his 15 Premier League assists are the top mark for the English top-flight.
Chelsea have been hit with a two-window transfer ban as a result of irregularities regarding their recruitment of young players, and Hazard has been consistently linked with a move to Real Madrid.
Manager Maurizio Sarri has spoken about the rumours about his star man, admitting that he only wants to retain the player if his commitment to Chelsea’s cause cannot be doubted.
“I don’t know. If Hazard is thinking that history here is finished, then his mind it is finished,” the Italian said.
“I can try to speak to him but it is not easy. It’s not easy because of course I want Hazard, but I want Hazard, but I want Hazard with a very high level of motivation.”
They play Arsenal for that prize in Baku on May 29.
He added: “We were happy to finish third. We wanted more but our finishing was not good enough.
“We were in trouble a couple of weeks ago which shows the league is not easy but we showed character in finishing third and reaching the final of the Europa League,” the Spanish international defender concluded.