Blues owner Roman Abramovich is refusing to be rushed into making a decision about the club's next permanent manager, despite the clamour for caretaker boss Di Matteo to be rewarded for masterminding the greatest climax to a season in their history.
Reports suggest Abramovich would only be prepared to offer the Champions League-winning Di Matteo a one-year trial, something that would allow him to approach Pep Guardiola once the Barcelona boss completes his one-year sabbatical.
Gourlay told Chelsea TV: "We now need to sit down over the next week or two, or however long it takes, because we have to do what's right for the club.
"I know the fans will be pushing for Robbie.
"We're going to look at the season, look at what worked for us, look at the mistakes we made and put them right and take it forward."
Di Matteo's contract expires at the end of June and he is already being heavily linked with several other vacancies after ending Chelsea's agonising wait for Champions League glory - on top of their FA Cup triumph.
The likes of Aston Villa - his family home is in the midlands - as well as former club Lazio, and even Liverpool, have been mentioned as possible suitors.
The Italian had been scheduled to play in the BMW PGA Championship Pro-Am golf tournament at Wentworth on Wednesday before flying to Barbados at the end of the week for the British Airways Football Legends Invitational on Saturday and Sunday.
He was then expected to take the family holiday he has craved ever since being handed the reins at Chelsea three months ago.
Di Matteo may want to know his fate before then, while the Blues are looking to have their next manager in place before they fly to the United States for a pre-season tour on July 15.
Whether Di Matteo would accept a one-year deal - or even a longer one with the spectre of Guardiola looming over him were he to be offered a longer contract - remains to be seen.
Watch: Drogba says he is leaving Chelsea.. More Videos
There was also fresh uncertainty tonight [Tuesday] over the future of Di Matteo's fellow European Cup hero Didier Drogba.
The legitimacy of quotes attributed to the striker confirming he was quitting the club were called into question and Gourlay insisted Chelsea still planned to try to convince him to stay.
"Conversations with Didier have been going on for months and still are," he said.
"He's made it clear he loves Chelsea and loves everything he's achieved at the club.
"Once we're ready to make an announcement, we'll do so."
Reports have suggested Drogba has already agreed to join Shanghai Shenhua in a £250,000-a-week deal and that Abramovich may need to pay the Chinese club compensation to keep the 34-year-old.
Drogba snubbed the offer of a one-year extension earlier this season, while Chelsea refused to bow to his demands for a two-year deal.
The deadlock was allowed to continue right up until Saturday's final, which saw Drogba once again prove he was the man for the big occasion with a dramatic late equaliser and winning penalty shootout strike against Bayern Munich.
Chelsea appeared to have decided they were ready to move on from Drogba and build what has often been referred to as a "hungry, young team", one more in the mould of vanquished European champions Barcelona.
One man unlikely to shed a tear at Drogba's leaving party is Fernando Torres, the man billionaire Abramovich spent a record £50million on as the Ivorian's long-term replacement.
Torres became the latest Chelsea striker to be put in his place by Drogba and his frustrations boiled over after they were crowned kings of Europe, the 28-year-old attacking the club's treatment of him and threatening to quit.
The Spain star was seeking reassurance over his future role, one that could well be more prominent once Drogba is out of the picture.
Gourlay said: "I'd be surprised if Fernando, who's been awesome, didn't want more time on the field, every player does.
"Torres came on when we were behind and played a big part to help us win the Champions League.
"It must have been very difficult for Robbie, and for the guys on the sidelines.
"It was the biggest game in our history so there were different levels of emotions all over the pitch - you have to take these things into account."
It is doubtful Chelsea will not move to replace Drogba, and they have long been linked with a host of top strikers, including Radamel Falcao, Hulk and Edinson Cavani.
Their Champions League win also gave Eden Hazard food for thought after the Lille playmaker looked set to join one of the Manchester clubs, while Sao Paulo's Lucas Moura and Bayer Leverkusen's Andre Schurrle are other reported targets.