Liverpool chief executive has admitted that the club are considering a friendly with Major League Soccer side Los Angeles Galaxy.
Steven Gerrard now plays for the MLS outfit after ending a 17-year career with Liverpool in the summer and Ayre believes that the link provided by the 35-year-old may pave the way for a pre-season game in the US.
When asked by BBC Sport whether a game against Gerrard's current club is likely, Ayre said: "That's something we have on our radar of ideas.
"Steven is back in Liverpool at the moment, so I'm sure we can have a chance to see what he thinks."
Gerrard was unable to help LA Galaxy defend their MLS title in his first season with the club as they lost in the playoffs to Seattle Sounders.