Mignolet has blown hot and cold for Liverpool for some time and was dropped earlier this season only to be recalled due to an injury to Australian Brad Jones.
Ryan, 22, has been in great form in the Asian Cup for Australia, making some impressive saves and generally looking a class act between the posts.
According to reports in various British newspapers, Liverpool manager Brendon Rogers is very interested in acquiring Ryan, who plays in Belgium with Club Brugge.
Brugge's former sporting director Arnar Gretarsson told the Daily Telegraph that the young keeper is keen on a move to England.
"I think he will move to a bigger team, possibly for next season," he told the paper.
The Mirror, Express and Guardian have also linked the Reds to the keeper.