Martin Baturina has attracted interest from several major European clubs, such as PSG, Manchester United, Manchester City, Atletico, Barcelona, and Real Madrid. This interest was particularly notable at the close of the last summer transfer window. Nonetheless, Dinamo Zagreb opted to keep Baturina even before Zvonimir Boban took over as the new head of the club. Fiorentina made a concerted effort to acquire him, initially proposing 12 million euros plus bonuses, and subsequently increasing the offer to 15 million euros, eventually reaching up to 20 million euros with bonuses. Additionally, Fiorentina proposed giving Dinamo 10% of any future transfer fee. Despite these offers, Dinamo declined all proposals, resulting in Baturina staying at the club.

During the winter transfer window, Martin Baturina was a target for PSG. However, the situation has changed, and now Eintracht Frankfurt is the club showing significant interest.

PSG is reportedly showing serious interest in signing Martin Baturina from Dinamo Zagreb. Various sources have indicated that negotiations are already at an advanced stage, which could potentially result in a deal by January. PSG seems to be making concrete efforts to secure his signature. They are prepared to purchase Baturina in January but plan to leave him at Maksimir until June, allowing him to complete the season in Croatia before transitioning to Parc des Princes. The reported fee is approximately €25 million. Some sources suggest that this amount includes bonuses, while others believe it is a fixed sum; in either case, it is a figure that Dinamo would likely accept.