According to WAZ, talks over extending the 29-year-old's current deal, which runs until 2028, are set to take place in the coming weeks. Anton is said to be happy in Dortmund, but his form has not gone unnoticed elsewhere, with clubs from abroad also keeping tabs on the centre-back.
Anton joined Borussia Dortmund from VfB Stuttgart, where he had established himself as one of the Bundesliga's more dependable defenders, and has since become a regular starter and a senior voice within the squad.
His performances for both club and country have continued to draw admiring glances from beyond Germany, with his composure in possession and organisational qualities at the back seen as particular strengths.
Atletico Madrid and Manchester United have both been linked with the Germany international, whose performances at the heart of Dortmund's defence have made him one of the more reliable figures in the squad.
Whether that interest develops into anything concrete is likely to depend in part on how quickly the extension talks progress, with Dortmund keen to remove any uncertainty before speculation builds further over the rest of the summer.
Dortmund's approach reflects a broader effort to lock down key squad members this summer, with the club keen to avoid instability at the back heading into the new season. Anton has established himself as first-choice in the heart of defence since arriving at the club, and the proposed pay increase would recognise both his importance to the side and the growing external interest in his services.
The move also fits a pattern at Dortmund of moving early to secure defensive personnel considered central to the head coach's plans, rather than allowing contract situations to drift into their final year and invite exactly the kind of speculation now surrounding Anton.
Nothing is expected to be resolved quickly, however, with the coming weeks seen as the starting point for what could be extended negotiations between the club and the player's representatives.