With regular 'keeper Danny Vukovic suspended for the first seven games of the season, the Mariners are understood to have approached the former Aston Villa custodian about a short term deal.
Fairfax Newspapers reported Bosnich, 36, had discussions with the club's deputy chairman Peter Turnbull, when he was in Australia attending the FIFA Congress.
While coach Lawrie McKinna denied there had been an approach to Bosnich he said the club would happily consider him.
"He's been a quality goalkeeper over the years," McKinna said.
"You never say never and Mark Bosnich was one of the best keepers in the world on his day, and if he was fit and back in shape, of course you'd look at him."
Bosnich struggled for regular first team football after moving from Aston Villa to Manchester United in 1999, then briefly Chelsea.
Bosnich last played a professional match in 2002 but trained with the Queens Park Rangers last year.