Reports suggest owner Roman 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.
Source: PA
Source: PA