Moore has already made seven summer signings, including Millers old boys Paul Warne and Rob Scott, and sees Pollitt as been able to provide perfect competition for the Latics' Aussie shotstopper Les Pogliacomi.
Moore said: "We're just a little short of his financial package, but as time goes on you never know - it's a bit like a game of poker.
"The longer you leave it the more you can win. We now have a new goalkeeping coach in Graham Brown and I'm hoping he can help Les to get back to his usual consistent form.
"We definitely need two keepers pushing for the number one spot."
Oldham have also been linked with a move for Stoke's out-of-contract forward Gifton Noel-Williams.