Moro, 22, is another major talent off the Zagreb production line and has attracted great interest in eastern Europe.
The Croatian club received a €7m offer from Dynamo Kyiv for Moro and were ready to accept it, but he turned down the move.
11-time Russian champions Dynamo Moscow have now made a move, proposing a structured deal that could reach €10m.
Moro has agreed personal terms with the Muscovites and will sign a long-term deal if talks conclude successfully.
Negotiations are not yet complete but a source familiar with the situation said they are ‘moving calmly towards a good conclusion’.
The new Modric?
Moro, a central midfielder by trade, has already made 114 appearances for the Dinamo Zagreb first team.
His excellent passing ability has led to natural comparisons with his compatriot Luka Modric.
Moro is also a Croatian youth international and is certain to become a part of the senior squad soon.