The veteran centre-back is looking for a new club after he left Crystal Palace at the end of last season when his contract expired.
Several clubs in the Premier League and the Championship have been looking at the 35-year-old defender as an experienced option.
Southampton are in the market to bring in a replacement for Jannik Vestergaard who left for Leicester City this month.
Cahill has been linked with a move to the Saints and there are claims that they have offered him a contract.
But those claims have been rubbished and Southampton have made no such offers to the veteran defender.
It is unclear whether they are interested in him, but Cahill has no offer on his table from the Premier League side.
Bournemouth are still being tipped as his likely destination before the end of the transfer window.
The Championship club have been in talks with Cahill over signing him on a free transfer this summer.
