The 31-year-old took 20 wickets as his country retained the Ashes this summer in a drawn series against England.

Hampshire have been linked with Lyon in recent weeks, who has previously played for Worcestershire in county cricket.

"He was very keen when we met with him earlier this season at the Ageas Bowl," Hampshire first-team manager Adrian Birrell told BBC Radio Solent.

"We sold him the concept of trying to win the County Championship with an off-spinner and create a bit of history.

"But there's obviously been a lot of mileage under his belt since that conversation so he is mulling things over.

"Failing him, we will of course find someone else who can do a similar role."

Australia's winter features two Tests at home against Pakistan before a three-match series with New Zealand which finishes in January, so Lyon could be available from the start of next season in April.