Shomurodov, 25, is joint fourth in the top scorer charts for this season’s Russian Premier League with 11 goals.
The talented centre-forward isn’t just a goal scorer either, having delivered seven league assists this term.
His form has led to an Belgian club Gent submitting an offer, proposing €5m to be paid in installments.
Rostov dismissed the offer and would want at least €10m to sell Shomurodov.
Gent are unlikely to try again, having set a maximum budget of €6m for a new target man who is at least 1.90m tall.