The 21-year-old, who secured an eighth successive Scottish Premiership title with the Bhoys over the weekend, has a contract with the Glasgow club until 2023.
However, the Mirror has reported that Inter and Napoli have put Tierney’s name high on their lists of targets for the summer.
The Italian clubs could test Celtic’s determination to keep their highly-rated academy product in Scotland.
Leicester City, led by former Hoops manager Brendan Rodgers, had also been linked with the left-back but now look unlikely to make an approach with Ben Chilwell set to stay at the King Power Stadium.
Tierney will have a double hernia operation over the summer, which will see him sidelined for Scotland’s Euro 2020 qualifiers against Cyprus and Belgium.
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