Roberto Di Matteo is currently in temporary charge of the Blues and has guided them to Champions League and FA Cup glory.
Fans and members of the first-team squad have called for the Italian to be handed the reins on a permanent basis, having taken over from Andre Villas-Boas in March.
Gourlay was full of praise for the former West Bromwich Albion boss, but stressed the club will not be rushed into making their choice.
"As we've said exactly from the day Robbie was given the job as interim coach, let's get through to the end of the season, we set ourselves goals and then when that season ends then we'll sit down and discuss things," Gourlay told Sky Sports News.
"Whilst we hoped to get to Munich we didn't know at the time we would get there so we just asked Robbie to give us his best and see where we went.
"So now we have to sit down over the next week or two, or however long it takes, because we've got to do what is right for the football club.
"We will look at the season, look what worked for us, look at the mistakes we made, put them right and then take it forward.
"I know the fans will be pushing for Robbie, but we're not jumping into anything rash.
"He has done fantastically well and I'm very proud of him and what he has achieved. But we will stick with what we said and sit down and talk things through and work things out."
