A similar operation was being prepared by the Russian command, but was thwarted by the need to protect Romania. From Russian Wikipedia (there is no English version of the article):
"The Russian command returned to the plan to seize the Bosphorus in 1915, already during World War I. On May 16 (29), 1916, after lengthy diplomatic correspondence and negotiations, between Great Britain, France and, somewhat later, the Russian Empire and Italy, a secret "Agreement on the partition of Asian Turkey" was concluded with secret protocols, better known as the Sykes Agreement – Pico. According to him, the rights of Russia to Constantinople and the straits were finally confirmed, as well as the vast conquered territory of Western (Turkish) Armenia and part of Kurdistan went into the direct possession of Russia.
At the end of November 1916, the command planned the "Bosphorus Operation". The project was sent for approval to the Headquarters, where it received full support. To carry out the operation, a separate Black Sea naval division was created under the command of General A.A. Svechin, staffed with experienced front-line soldiers, St. George's cavaliers. The general command of the troops involved in the operation was entrusted to the commander of the Black Sea Fleet, Vice Admiral A. V. Kolchak.
From Kolchak's interrogation:
According to the plan of this Bosphorus operation, one land unit, a strike-type division, was at my immediate disposal, a frame of which was sent to me from the front and one of the best officers of the General Staff, General Svechin; Colonel of the General Staff Verkhovsky was appointed chief of staff. This division was preparing under my direct supervision and had to be thrown by the first landing force on the enemy coast in order to immediately settle on it and provide a landing site for the next troops that were to follow them. So all this preparation of work was going on until the onset of a coup d'état at the end of February. <…> The Bosphorus operation was supposed to be in the spring of 1917.
But the operation had to be postponed due to the fact that two army corps had to be sent to the Romanian front, since the Romanian army was completely unprepared to conduct hostilities and at the same time transport ships intended for the operation were involved. The decisive blow was planned for April 1917, but because of the February Revolution, the operation did not take place.
