I don't know about a religious war, but Russia negotiated with Britain early in the First World War to receive Constantinople as a war aim if the entente successfully defeated the Ottoman Empire.

The negotiations were part of a series of war promises that Britain made over what was to be done with Ottoman territory. Of these other negotiations the Sykes-Picot agreement is probably the most famous.

Both Sykes-Picot and the Russian agreement over Constantinople were negotiated in secret and revealed before the end of the war by the Bolsheviks.

For all the attention these agreements receive in the popular imagination, the actual borders of the middle east post-World War I were ultimately drawn as a result of the Treaty of Sevres, the Treaty of Lausanne, the San Remo Conference, the Cairo Conference, and the confirmation by the League of Nations of a combination of the above.

As far as I know, during the reign of Catherine the great, plans were made to retake Constantinople and one of her grandsons was even called Constantine because of this (he was meant to be the ruler of the city). This idea didn't die with her and developed by the end of 19th century into "protect Balkan Christians who are suffering under the Turkish reign" state policy. Coming into WWI Russia was still making moves in order to retake the city, at least on paper.