Di Matteo has been in temporary charge for three months and has led the west London outfit to the FA Cup and a maiden Champions League success.
Buck told The Mail on Sunday: “He’s done an amazing job, he’s enabled these players to get back their confidence that they used to have and need to perform.
“We’ve put [the appointment] aside for the last five-to-eight weeks, now in the next few weeks we have to sit down, figure it out and do what’s best for Chelsea.
“Roberto is certainly in the mix and he’s done a great job for us and he has to have serious consideration.”
When asked if an appointment would be made before Chelsea's pre-season tour in mid-July, Buck replied: “Surely.”
Chief executive Ron Gourlay also praised Di Matteo highly, but did not make any promises that the Italian would be rewarded with the full-time job.
He added: “It's been an incredible few months and a great ending last night with winning the trophy.
“It's been an up-and-down season. We started reasonably well but we had a bad period around November, December, January.
“The performances and results weren't there so we had to make the change, we brought Robbie in as interim manager until the end of the season and we've seen a phenomenal change and a run of results which finished last night with winning the Champions League.
“There's a number of things we've got to look at and we'll review where we are and take it from there, but it's a phenomenal turnaround really.”