In Call Of Duty 4, proof of this can be found in the opening cutscene of “All Ghillied Up”, where Price references Chernobyl and how the Ultranationalists terrorists use its nuclear fuel even a decade after the disaster. Chernobyl happened in 1986, and thus All Ghillied Up is set in 1996, 10 years after. The mission takes place 15 years prior to the main storyline, thus 2011.

However, it has also been argued that the game actually takes place in 2010. Unused code for “All Ghillied Up” (which is included in the mod tools) states that the mission actually takes place in 1995. While some think it takes place in 1992, as 2007 was the game’s release date.

So, the Modern Warfare 2 would have started in 2016, since it says 5 years later the story of the CoD4. There is also another solid prove where Modern Warfare 3 starts in 2016, just hook up the single-player campaign “Black Tuesday” where if you look at the TV, the title says “BATTLE FOR NEW YORK – America’s last stand?” and it also says “MAY 13, 2016″. The news most likely is a CNN, thought since USA is under World War III against Russians, therefore I think the CNN studio is mostly likely forced to shutdown.

As far as I know, it’s made ambiguous so that it’s always about five minutes in the future for the main audience (us).

(Cookies to those who got the reference, however unlikely that might be over here.)

e: Wow, The Sents’s answer pretty much pointed out the implied timeframe. But I still think they deliberately not mention it explicitly, so even people who play MW1 now still can think of it as sometime in the future.