But they are not done there, having had bids turned down for other attacking players - including Wigan's Victor Moses - as well as being heavily linked with Marseille right-back Cesar Azpilicueta.
Speaking at the end of the European champions' US tour, Gourlay said: "While we ended with a very strong season, it was clear that there were some areas where we did have to strengthen, so we knew we were always going to have to do that.
"If the right players become available at the right time, we will sign them. We've done that and we are still continuing to look at one or two positions and we will see how that develops over the next couple of weeks."
Chelsea's billionaire owner, Roman Abramovich, was a visible presence in America during the past fortnight and Gourlay added: "Internationally, we have grown and grown in the last four years and I wanted him to be here to see just how his club has developed."