Cook picked up individual and team eventing bronze on her Olympic bow aboard Miners Frolic at Beijing in 2008, before upgrading to silver in the latter at London 2012.
That would suggest Cook is a good bet for Rio 2016 and, despite being almost 45 by the time the Games roll around, she fully intends to throw her name in the hat for selection.
Her latest ride, De Novo News, finished ninth at the Land Rover Burghley Horse Trials last year. However, an early mistake ruled them out of the reckoning at Badminton in May.
The World Equestrian Games, which start on August 23, are Cook’s next aim and she admits a third Olympic appearance could rest on whether she travels to Normandy or not.
She said: “I have been doing eventing for a long time but after London I decided that I wanted to carry on at that level of competition and aim for Rio.
“It’s another four-year cycle and a lot can happen but De Novo is going well and there are also some promising young horses coming up behind him so things are looking good.
“It would have been good to have got a result on the course at Badminton but I would like to think that I am being considered for the worlds.
“It’s the start of qualification for Rio – it all starts afresh this year – so it’s important from the selectors’ point of view to select a team with experience and capable of going for gold.
“But there is also a sense of building towards Rio. We should find out in the next couple of weeks, so we are waiting for that announcement.”
Cook is certainly no stranger to the World Equestrian Games, having won team gold twice in addition to her three Olympic medals – the first in The Hague in 1994 and the second in Kentucky in 2010.
Selection for this year’s Games would rule her out of the Land Rover Burghley Horse Trials that follow.
n The multi-award winning Land Rover Burghley Horse Trials (September 4-7) has been established as a major international equestrian and social event in the autumn sporting calendar for more than 50 years. For more information visit www.burghley-horse.co.uk