Slaven Bilic wanted to sign 27-year-old Orsic in January and the Baggies made a €7m offer.
Zagreb responded by asking for €10m and West Brom withdrew, considering the price too high.
West Brom have now been promoted to the Premier League and are back for Orsic with a €9.5m bid.
The Croatian champions have yet to respond as they seriously consider the offer.
La Liga side Sevilla are known to like Orsic but have not yet sent an official bid to Dinamo.
There is a feeling that Sevilla may follow up on their interest and if so, that could alter the situation.
Orsic is coming off a fantastic season for Zagreb in which he scored 21 and assisted 10 goals in 42 appearances.
In the group stage of the Champions League, Orsic scored a hat-trick in Dinamo’s 4-0 win over Atalanta.