Gourlay reiterated that Ancelotti's contract runs for a further season, and said the club understood the league title could not be won every year. However, when asked directly if Ancelotti would stay on, Gourlay did not give a straight answer.
'All you can say is that Carlo has a contract with the club until 2012,' he said on Radio Five Live's Sportsweek.
Leading the line: Ancelotti hasn't been offered any guarantees about his future at Stamford Bridge
'We're delighted with Carlo and what he's achieved so far. These things can be pretty fickle. Carlo has come in and won the double last season. Yes, the expectations are high, but they are high at many clubs around Europe and we've got to be realistic.
'Let's see where we are at the end of May.'
Chelsea are fourth in the Barclays Premier League after run of poor results saw them surrender a once-comfortable lead at the top of the table. They can go third later today if they beat Manchester City to leapfrog them in the table.
Gourlay did give an endorsement to Ancelotti's qualities as a manager.
No dummy: Ancelotti delivered the club's first Double last season
'Carlos is a world class coach,' he said. 'You look at his record and it speaks for itself. His record at Chelsea in a short time, winning the double in the first season in a new league, coming out of Italy, is a great feat.
'This is a strong, competitive league, but his knowledge of the game is second to none and he holds a dressing room well.
'He's won the Champions League twice as a coach and twice as a player so he's been there and done it.
'We understand it is very, very difficult to win trophies every year. What's very important for this club is to be competiting for trophies in the latter stages of every competition."
Gourlay did not offer specific targets for Chelsea to meet over the remainder of this season.
'We're realistic,' he said. 'You can't win the double, you can't win the treble every year. But we want to see progress in the club every year.
'All I can say is that Carlo has a contract until 2012. We were delighted with last season, and we're happy with the way it's going this season.
'We're coming to the sharp end now, we've got 10 games left in the league and we have a fantastic draw (against Manchester United) in the Champions League. Our expectations are high and we've got to keep driving the club forward."
Gourlay also said owner Roman Abramovich's commitment to the club is as strong as ever, as highlighted by his investment of ?70million in Fernando Torres and David Luiz in January.
'Roman is fabulous in his support," Gourlay said. 'He likes to be involved in the process, he likes to understand our decision-making and process and, to be honest, that's the best way for the club to move forward.' ?50m Torres promises a first Chelsea goal to mark his birthdayKenny Dalglish: If Terry was wrong man a year ago, why is he right now? Mancini backing ?50m striker Torres to come goodAll the latest Chelsea news, features and opinion
Explore more:People: Roman Abramovich, Carlo Ancelotti Places: Italy, Europe