I'm quite confused as to how so much can have been written in this thread and yet no one has mentioned any of the key treaties involved. Frankly I would ignore what has been written so far as its basically irrelevant to your question and seems quite ill-informed.

As part of the Constantinople Agreement the Triple Entente absolutely intended to seize Constantinople after the war, as it was promised to Russia. It formed the Russian component of the dividing of the Ottoman empire in the event of victory, along with the more famous Sykes Picot agreement for the British and the French. When Russia dropped out of the war with the communist revolution and the treaty of Brest Litovsk they were naturally excluded from gaining the promised territories. (Interestingly it was the Bolsheviks who first revealed France and Britain's theretofore secret imperial plans by publishing the details of Sykes Picot.)

The next major treaty in question was the actual peace negotiation with the Ottomans, the Treaty of Sevres. This called for the complete breakup of Anatolia into national spheres of influence and control with Istanbul under international control.

The Turkish War of Independence, however, prevented the treaty from being ratified and carried out, but Constantinople was in fact occupied from the end of the war until 1923 when the Treaty of Lausanne established the borders of modern Turkey, recognized the new government, and ended the occupation of Istanbul.

As you may know, Germany and Austria Hungary, the other Central Powers, were forced to relinquish control of territory which the dominant ethnicity of each country was not the majority. For Germany this meant it's limited overseas holdings and it's periphery areas such as the Sudetenland, and Austria Hungary it's various Balkan holdings. To clarify, no ethnic group held a majority in Austria Hungary, with the Magyars (Hungarians) forming the plurality and the Austrians a close second. So in order to respect the diverse ethnic boundaries Austria Hungary was carved into multiple countries with a majority ethnic group (with the exception of Czechoslovakia). Now how does this ethno-centric restructuring relate to the Ottoman Empire? The dominant ethnic group of the Empire was, predictably, the Ottoman Turks, who largely resided in modern day Turkey. Like the other losers of the Central Powers, the Ottomans were forced to relinquish control of what were perceived as it's "colonies", or areas in which Turks were not the dominant ethnic group but exercised control. The ceded areas in turn became the French and British mandates in the Middle East.

So your next question is probably why such emphasis on borders which reflected ethnic divisions? The Allied leadership of the time aimed to create a peace which would last after four arduous years of war. It was also a belief among Allied leadership, particularly Woodrow Wilson, that ethnic conflicts and a lack of ethnic self determination was the root of many conflicts. One can look at Wilson's famed 14 points in which the fifth states that the peace settlement should aim to establish, "V. A free, open-minded, and absolutely impartial adjustment of all colonial claims, based upon a strict observance of the principle that in determining all such questions of sovereignty the interests of the populations concerned must have equal weight with the equitable claims of the government whose title is to be determined." As a result, and to create a lasting peace, the losing nations lost territory in accordance with the territories ethnic distributions.

So to finally answer your question, the Allies did not consider the permanent seizure of Istanbul because it not only ran against the ideas of ethnic determination (as the Turks held a firm majority in what was largely considered their capital), but also would have served to weaken and anger the newly established Turkey.

The Fourteen Points: http://avalon.law.yale.edu/20th_century/wilson14.asp

Also I understand this answer is relatively poorly cited, as I am on my mobile. If it does not meet the subs standards I understand it may be deleted. Please understand it was a labor of love.

Edit: Spelling and u/FiveShipsApproaching has pointed out some pretty large oversights in my answer as well.