The Reds are looking to increase the capacity of their current stadium after shelving plans to move grounds last year, and Ayre has said that the club are currently at the right stage of their schedule.
"In order to extend Anfield, we need to acquire a bunch of privately-owned property around the stadium. We're making really good progress with that," Ayre told Sports Illustrated.
"We have a meeting coming up in the next few weeks with the city council and ourselves and stakeholders. We said some months back it would take several months to improve that property acquisition situation. We're definitely on target so far.
"There are two or three hoops to go through. The first is property acquisition, the second will be planning and the third will be to build the thing. I would guess our next announcement on it will come sometime in May or June.
"I remember the first time [club owners] John Henry and Tom Werner came to look at Liverpool before they bought it. I was the person showing them around. When we went into Anfield, John said to me: 'This is like Fenway [Park]. It's the same feeling. Why would we want to build a new stadium?'"
The Reds were bought by Fenway Sports Group in October 2010.