The Blues are celebrating becoming European champions for the first time in the club's history following the penalty shoot-out victory over Bayern Munich on Saturday night.
Di Matteo led Chelsea to Champions League glory after replacing Andre Villas-Boas in early March and he also secured the FA Cup final at Liverpool's expense earlier this month.
Success in the Allianz Arena has intensified calls for the Italian to be handed the manager's job on a permanent basis after lifting morale following Villas-Boas' departure.
Buck says the club will not rush into a decision regarding who will be in charge for next season, but acknowledged the strength of Di Matteo's claims to stay on.
"He's done an amazing job, Robbie," Buck told Sky Sports News. "He's enabled these players to get back the confidence they used to have, which they need to perform.
"He's really got the players to perform and we're really proud of him."
Regarding the managerial situation, Buck added: "We've put that aside for the last six, eight weeks to concentrate on Barcelona, the FA Cup, Bayern Munich.
"In the next few weeks, we will have to sit down and figure that out and do what's best for Chelsea, and we will.
"Robbie is certainly in the mix. He's done a great job for us and he has to have serious consideration.
"It will be sooner rather than later because we really need to get the new manager on board before we can start talking about players.
"We want to do what's best for Chelsea. We hope to do it relatively promptly but if it drags on a little bit longer than we expect in order to do the right thing for Chelsea then we will."
When asked if an appointment would be made before the pre-season tour to the United States, Buck replied: "Surely."
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