There is a reluctance from owners Fenway Sports Group to move away from Anfield to a new build in Stanley Park because of the financial implications, with an investment of £300million-plus only delivering an extra 15,000 seats.
Remaining at Anfield has its own problems, however, as expansion would infringe on the 'right to light' homeowners in the surrounding area are entitled to.
FSG have been criticised for not coming up with a definitive plan in the 19 months they have been in charge but Ayre stressed they were making headway.
"There is progress and we are still in dialogue on both fronts," he told the Liverpool Echo.
"We have more dialogue going with the Anfield residents than we ever have, as with other stakeholders in and around Anfield.
"I think it's also fair to say that we are already fairly well down the line with a couple of major brands who have shown significant interest in naming rights for a new stadium.
"We want to explore both options to a solution and I think it's fair to say if we continue making progress in that area, it might move faster than we originally anticipated.
"Part of the problem is that people assume that because we don't make a major announcement that nothing's gone on and no progress has been made.
"It's all right for people to say 'Liverpool's a big football club - 60,000 seats, why don't you just go and get on with it?' but go and look at the economics of that - a £300m build for 15,000 new seats.
"It's pretty hard to make that stack up. The work is going on and a decision will be announced when we've got certainty."