The Blues have reached the finals of the FA Cup and Champions League under the Italian's guidance.
However, despite admitting that he is pleased with Di Matteo's work, Gourlay has refused to comment on whether the 41-year-old will be offered the job on a permanent basis.
"It's very important that we follow out what we said originally," Gourlay told talkSPORT. "We appointed Robbie as an interim manager until the end of the season.
"Since Robbie took over we've had 15 games, 10 wins, four draws and one defeat. It's been a good turnaround. We just went through a period where performances and results weren't very good and we've managed to turn that around with the same team of players.
"We've got to focus on the remaining six games that we have between now and the end of the season and I know it's the old cliche, 'one game at a time', but honestly that's the way that we've set ourselves up since Robbie took over and it's working very, very well."
Chelsea are currently sixth in the Premier League table.