Chelsea chairman Bruce Buck says Roberto Di Matteo is being strongly considered for the manager's job after winning the Champions League.
Di Matteo has also won the FA Cup as interim boss, and Buck told Sky Sports News: "He is certainly in the mix.
"He's done a great job and has to have serious consideration. He's really got the team performing."
Blues legend Gianfranco Zola said: "He should've been offered the job before the final for what he's achieved."
Buck confirmed Di Matteo will learn his fate "sooner rather than later", knowing Chelsea must move on the manager's position before they can establish summer transfer targets.
Chelsea are a more attractive proposition following Saturday night's penalty shoot-out win over Bayern Munich, which ensures they will play in the competition next season despite finishing sixth in the Premier League.
Former MK Dons and West Brom boss Di Matteo, 41, was promoted from assistant to interim boss following the failed "project" of Andre Villas-Boas.
He took over between the two legs of the last-16 tie against Napoli and oversaw the overturning of a two-goal deficit. He also led the Blues to wins over Benfica in the quarter-finals and holders Barcelona in the semis.
"Robbie has done an amazing job," Buck added. "He has enabled the players to get back the confidence they used to have. He's really got them performing.
"We've put (managerial speculation) aside for the last six or eight weeks, concentrating on Barcelona, the FA Cup and Bayern Munich, but I think now we have to sit down and figure that out."
Zola is in no doubt that his former Chelsea team-mate Roberto Di Matteo should be made permanent manager.
Saturday's win in Munich comes two weeks after the Blues secured the FA Cup by beating Liverpool at Wembley.
And Zola told BBC Radio 5 live's Sportsweek: "He is one of the guys who has created Chelsea's fortunes.
"Wherever he goes, he is now a Chelsea legend as a player and as a manager."
Blues chief executive Ron Gourlay insists the club will take their time over the decision, but confirmed talks will take place now that the season has been completed.
"There is no time scale on this," he said. "We'll sit down over the next few days and discuss things.
"We are aware of the pressure that is on the board and the owner to make the right decision but we've said from day one we'd get through the season first and Robbie has been fine with that.
"We didn't want to put any extra pressure on the team."
Former Blues manager Avram Grant, who left Stamford Bridge after leading them to a Champions League final penalty shoot-out defeat by Manchester United in 2008, agrees that the Italian is the right man to take the club forward.
"I'm not the guy who makes the decisions at Chelsea but he's the man," Grant told the Sun on Sunday.
"Sometimes when a club takes on a coach who is not so famous and the team is not doing so well everybody would say it's his fault.
"So when it goes well, he should get the credit. It's justice."