The Saints narrowly saved themselves from getting relegated last season, and the 28-year-old played a huge part in their survival battle.
McCarthy joined the Saints from Crystal Palace in 2016, and struggled to get regular games. However, he replaced the error-prone Fraser Forster in January, and made a strong impact.
The former Crystal Palace star started only 23 games, and was named the south coast side’s Player of the Year, such was his influence in the side.
Spurs chief Mauricio Pochettino is looking for competition for Hugo Lloris, and finds him an able deputy for the role.
Liverpool manager Jurgen Klopp is also keeping a close eye on McCarthy’s situation following Loris Karius’s Champions League horror-show.
McCarthy will be a free agent next summer and he will sign a contract extension if the Saints match the £3m-a-year deal they gave Forster last year.
The report adds that he is demanding a bumper £60,000-a-week contract to stay at Southampton.