Anton, 29, was a key figure at Dortmund last season after joining from VfB Stuttgart for €22.5m in 2024, making 32 Bundesliga appearances and nine in the Champions League.
He can play at right-back as well as in central defence — a versatility Carrick values — and is understood to be a composed, authoritative presence in the Dortmund dressing room. According to Ruhr Nachrichten, Carrick can "easily envisage" Anton in his squad.
Manchester United's renewed interest in central defence has been driven by concerns over the fitness records of Lisandro Martínez and Matthijs de Ligt, both of whom missed significant time through injury in 2025-26. Harry Maguire signed a new one-year deal, but Carrick wants more reliable options alongside Leny Yoro.
Borussia Dortmund have no intention of selling. The German club want to tie Anton down to a contract extension before the window opens in earnest, with his current deal running to June 2028. Anton himself is not understood to be pushing for an exit.
A bid of £35m would represent a meaningful profit on Dortmund's original €22.5m investment, which may test their resolve depending on the strength of United's approach. Central defence is nonetheless understood to be lower on Carrick's priority list than midfield reinforcement and a new left-back.
Anton is currently representing Germany at the 2026 World Cup and a strong tournament showing could increase both his market value and the number of clubs pursuing him, adding urgency to United's thinking if they decide to move formally.