The 33-year-old has been contracted to the Saints since 2016, making a total of 139 appearances in all competitions, but the South-coast outfit have now been relegated to the Championship.
McCarthy is also now no more than third choice under Russell Martin, and all parties are now searching for a solution for the veteran stopper before the end of the summer transfer window.
According to the Evening Standard, former club Palace and Everton are looking to add the Englishman to their ranks after negotiations allegedly broke down with Luton Town.
Both clubs are in the market for a number two with Vicente Guaita pushing to leave Palace and Asmir Begovic having already left Everton for Queens Park Rangers.
With McCarthy having less than a year remaining on his contract and Southampton happy to reduce their wage bill, they are not expected to demand a substantial fee.
Staying on the subject of Everton and they reportedly still want to get a deal over the line for Leeds United winger Wilfried Gnonto.
On Monday morning, the Toffees announced that they had signed Jack Harrison from the Championship outfit, initially on a loan deal.
That development came after Everton had been heavily linked with Gnonto throughout the summer, the Italy international going as far as withdrawing his availability to represent Leeds in the second tier in a bid to force a move.
The Daily Mail claims that Sean Dyche is still interested in signing the 19-year-old as soon as possible.
Any deal is expected to be a loan with an option - voluntary or mandatory - to buy at a time when Leeds have already allowed seven players to take such a route out of Elland Road.
Meanwhile, Al-Ahli are allegedly on the brink of continuing their spending spree after their return to the Saudi Pro League.
Last season's second-tier champions are one of the favourites to win the 2023-24 top flight after signing Edouard Mendy, Roger Ibanez, Franck Kessie, Allan Saint-Maximin, Riyad Mahrez and Roberto Firmino.
Those players contributed to Al-Ahli winning their opening fixture of the season on Friday, and it now appears that another defender will soon be joining their ranks.
Transfer expert Fabrizio Romano says that Al-Ahli have a deal in place with Atalanta BC to sign Turkey international Merih Demiral.
The 25-year-old, who has made a total of 102 outings for Juve and Atalanta since 2019, is said to have rejected proposals from two Premier League sides in order to move to the Middle East.