Morgan's future as England's white-ball captain is in question because he will be rotating himself this summer.
Morgan has been trying to manage injuries since leading them to 50-over World Cup glory.
I have the best interest of the team in mind. Morgan said that it's been that way for a long time.
The first of three one-dayers will be played by England on Friday.
There are three Twenty20 internationals against India and South Africa in July, followed by three more in August.
Morgan has had back and knee problems and is currently dealing with a thigh issue.
He was reluctant to commit to playing in all three of England's matches against the Dutch in Amstelveen because he would have to manage himself.
In the West Indies, Morgan played Saturday, Sunday and then injured himself before the game on the Wednesday.
Two international games resulted in that. I don't think I will be playing every England game.
That depends on how I get to that match. If I'm flying and everything is going well, I'll play, but if not, there's no need to try to duplicate that for a World Cup because it just doesn't happen. Yes, I'll be able to.
Matthew Mott, England's white-ball coach, said on Thursday that Morgan had a lot of great cricket ahead of him and his departure was a long way off.
Morgan is expected to lead the England team at the T20 World Cup in Australia in October and November.
Morgan, however, was reluctant to be drawn on whether he would lead England's defence of the 50-over World Cup they won at Lord's three years ago.
Are you talking about India? Morgan said that he needs to get to the T20 one first, having begun his international career with Ireland before moving to England.
I'm going to take it as it comes, managing my contribution, my body, and asking myself if I'm still contributing on and off the field.
I will be as honest as I can be with everyone. I feel like I can help in a World Cup win. It is an important drive for me.
Since taking over, I've trusted that method. It's a privilege to be in this position right now.