The Belgian international, who is a target for Real Madrid, will enter the final year of his Chelsea contract next season and has refused to sign an extension, meaning the London club could lose him for free if it does not sell him this year, Reuters reported.
“That would be good, that would be a nice last trophy,” Hazard told reporters on Monday.
“If it is my last game, I hope to bring the trophy.”
“It is a European competition, so for me, for the club, for the manager, for the fans, it is something important.
“When you play a final, it does not matter whether it is the Champions League, Europa League or League Cup, you just want to win, you just want to bring the trophy home and celebrate that.”
Hazard has won two Premier League titles, one FA Cup, one League Cup as well as the Europa League since joining Chelsea from Lille in 2012.
He scored 16 goals and created another 15 in the Premier League this season, as Chelsea finished third in the table, and said he was fully focused on the final despite the speculation over his future.
“At the moment, nothing has happened, so I can’t say anything. It’s in the hands of the clubs,” he said.
“But I can put it aside. I have done it during a full season right now, and I have played reasonably well.
“So I stay in that mode: Just thinking about football. After the final, we will see what happens.”
‘This year’ hopes
Real Madrid president Florentino Perez, meanwhile, confirmed on Monday the club is keen to sign Hazard this summer.
"I have a lot of interest in him coming to Madrid, I'm not going to lie, and I hope this year he can play here," Perez told Spanish radio station Onda Cero on Monday night, AFP reported.
"We have wanted to sign Hazard for several years and I hope he will come this year. Until now we have not achieved it, but this time his contract ends next year."
After a disappointing season, Madrid is expected to overhaul its squad this summer and Perez suggested the club's captain Sergio Ramos is considering a move.
Ramos and Perez argued after Madrid's Champions League defeat to Ajax in March, with Ramos reportedly telling Perez the team's failings were down to a failure to replace Cristiano Ronaldo.
Perez claimed on Tuesday that Ramos had been offered a move to China but said he had blocked the defender's departure.
"We met in my office and he told me he had a very good offer from a Chinese team but a rule there means they cannot pay for the transfer," Perez said.
"It was no more than that, it was a conversation that has no interest. It is impossible for Real Madrid to let its captain go for free. I told him it's impossible, nothing more."
Perez was also asked about the possibility of Madrid signing Kylian Mbappe or Neymar from Paris Saint-Germain.
"I have not spoken with Zinedine Zidane about either Mbappe or Neymar," said Perez, insisting he wants to maintain a good relationship with PSG.
"If we want a player of PSG, we will call the club's president."