Baturina, 21, represented Hajduk Split and RNK Split at youth level before moving to Dinamo Zagreb, and he has been a first-team player for the Croatian outfit since 2021.
The midfielder has represented his current side on 128 occasions in all competitions, scoring 16 goals and registering 32 assists in the process, while he has also been capped on five occasions by Croatia.
Baturina's playing style and nationality has seen him compared to the legendary Luka Modric, and according to journalist Patrick Berger, Dinamo Zagreb are facing a tough task to keep hold of him.
Berger claims that Real Madrid and Man United 'have positioned themselves' in the race for Baturina, while Atletico Madrid, Roma and Fiorentina are also said to be interested in his signature.
Real Madrid, Man United 'both interested' in Baturina
Dinamo Zagreb are in a strong position when it comes to the midfielder's future, as he has a contract with the Croatian giants until June 2028, while there is not thought to be a release clause in his deal.
However, if Real Madrid or Man United come calling next summer with a suitable offer, then it will be difficult for the Zagreb outfit to keep hold of him.
Baturina has already made eight appearances for Dinamo Zagreb during the 2024-25 campaign, providing four assists in his opening five league appearances of the season.
The Croatian also started against Bayern Munich in the Champions League on Tuesday night, but he could not prevent his side from suffering a 9-2 loss to the Bundesliga giants.
Real Madrid, Man United are both expected to sign a new midfielder in 2025
Real Madrid did not replace Toni Kroos over the summer following his retirement, but a new central midfielder is expected to be a priority for Carlo Ancelotti's team at the end of the current season.
Jude Bellingham has moved back into a deeper position in 2024-25 due to the arrival of Kylian Mbappe, but Los Blancos are short of numbers in the middle of midfield, and it is an area that the club are set to strengthen during next summer's transfer window.
Man United did bring in a new midfielder during the recent market, with Manuel Ugarte arriving from Paris Saint-Germain, but Scott McTominay left to join Napoli.
Casemiro is expected to move on next summer, which would put Erik ten Hag's side in the market for a new player in that area of the field.
Baturina certainly fits the brief when it comes to Sir Jim Ratcliffe's new transfer policy at Old Trafford, with the 20-time English champions now targeting young players as a part of a plan to eventually return to the top of English and European football.