The 39-year-old, who was initially offered new terms in May, is now a free agent and is set to hold talks over a move to Celtic.
Pompey chief executive David Lampitt told BBC Radio Solent: "We have done everything we possibly could.
"Our first preference would have been to keep hold of him, but unfortunately in these circumstances we can't always get over the line with these things.
"Both myself and (manager) Steve Cotterill tried to get to the point where we might be able to retain him as a player.
"He's been a great player for this club, a real asset over a number of years. We held out for him for as long as we could, but we've got three weeks until the start of the new season and we need to continue the re-building process and obviously part of that is getting a good goalkeeper in."