Morgan averaged 39.75 at a strike-rate of 93.89 in ODIs and 28.58 at a strike-rate of 136.17 in T20s for EnglandEngland's World Cup-winning captain Eoin Morgan is set to retire from international cricket.
An official announcement could be made on Tuesday.
Under Morgan, England won the 2019 World Cup and reached the top of the one-day and Twenty20 rankings.
The 35-year-old, who took charge of the T20 side in 2012 and one-day side in 2014, has struggled for form and fitness in recent times. Jos Buttler is the favourite to replace him.
England face India in a three-match T20 series starting on 7 July, while the T20 World Cup in Australia begins in October.
Morgan is England's leading run-scorer one-day and T20 cricket with 6,957 and 2,458 runs respectively.
His tally of 225 ODIs and 115 T20s is also an England record.
"He's done a remarkable job," England all-rounder Moeen Ali told BBC Test Match Special.
"It is a shame. It is strange to comprehend the side without him. Things move on and you have to get used to it, but it is sad.
"I'm not surprised at the same time because he is a very selfless person and probably is thinking about the team more than anything.
"We've been so strong over the years and he probably feels like his time is done and that he's given enough time for Jos, or whoever the captain is going to be, to embed his way."
Morgan took over from Alastair Cook as ODI captain and oversaw England's miserable 2015 World Cup campaign when they were knocked out in the group stages.
But he implemented a new, attacking approach which helped England break the record for the highest one-day total three times.
They achieved that feat most recently in making 498-4 against the Netherlands last week, but Morgan made ducks in his two innings in the series and missed the third ODI with a groin problem.
He has only one half-century in his past 26 white-ball innings for England.
"To change the mindset of a whole country and the way they play their cricket is a massive achievement - it is so difficult to do," Moeen said.
"To then be a very good captain on top of that, tactically on the field and to look after the players...
"There were so many times where people were caught on the boundary and they were like 'I should have just hit a single' and he was like 'no, no, next time you hit it out the ground'. We'd never come across a captain like that before."
