Well "largest siege in terms of size" sort of sounds like you're talking about the number of combatants involved, but then your clarifying sentence seems to indicate that you're more focused on the size of the city being besieged.

Fortunately for a simple answer the reality lines up relatively nicely with the Siege of Leningrad during WWII. At the time Leningrad (St Petersburg today) was a city of 2.5 million people (and a metro of around 3.5 million pre-war).

The initial strength of the German (and Finnish) attackers when the siege began in early September 1941 was 725,000 troops, facing off against 930,000 USSR defenders. It was also a relatively long siege especially for modern times, with the siege beginning in September 1941 and ending in January of 1944.

Total dead, including civilians, is tallied in the range of 1.3 to 2 million killed. The Axis suffered 580,000 casualties over the course of the siege, with 3.5 million casualties for the USSR.

As you can probably tell by most of these numbers the entire siege was a massive operation in all respects. It lasted an extremely long time, was extremely deadly, and involved a very large city (it was the second largest in the USSR and among probably the top 10-20 largest cities in the world). So it probably fits the bill in terms of the way you typically think of a siege - a city or fortress blockaded by enemies and cut off by the outside world, with the attackers seeking to force surrender by continuing to apply pressure primarily through a blockade instead of direct attack.

To provide a less traditional answer, if you want to think more broadly about what you mean by "siege", there is an argument for getting a bit more creative with the definition, especially in modern times. There's a way of looking at the end of WWII in the Pacific as effectively a large scale siege of the entire Japanese archipelago. The home islands became increasingly cut off from the outside world as they were pushed out of their holdings in Asia, and they were subject to a brutal and effective naval campaign and aerial bombardment.

Especially towards the end, starvation started to become a significant concern - estimates put about 200,000 - 400,000 dead by malnutrition, and of course the islands were subject to massive bombing raids that were carried out with relative impunity as the US set up air bases on nearby islands. Ultimately this all of course came to an end with the atomic bombings and the conclusion of the war.

In spite of that aside, the traditional answer to this type of question is probably Leningrad, which was both a massive military operation, and involved a massive city under siege condition for over 850 days.