Dwayne Bravo, Kieron Pollard, Sunil Narine and Marlon Samuels are others who could also be available.
West Indies' policy has been to only select players if they feature in the same format in domestic cricket.
And many have chosen not to play in West Indian one-day competitions.
That is because they often clash with lucrative overseas leagues such as the Big Bash.
The West Indies will travel to England next month, beginning a three-match Test series with a day-night match at Edgbaston on 17 August.
The squad for that series will be missing a host of big names as it has already been selected.
Following the Test series, the teams will meet in a Twenty20 match at Chester-le-Street on 16 September before the first of five one-day internationals at Old Trafford on 19 September.
In a statement, Cricket West Indies (CWI) said the "amnesty" with the players' union was "part of a wider strategy to be more inclusive and to improve player relations".
In 2014, a tour of India ended abruptly because of a dispute over pay, while the West Indies missed out on qualifying for the Champions Trophy earlier this year.
"We recognise that it is highly unlikely that we will now automatically qualify for the 2019 World Cup," said CWI chief executive Johnny Grave.
"So whilst the qualifying tournament has yet to be confirmed by ICC, we may only have eight ODIs against England and New Zealand in the next six months to prepare.
"It is crucial that we can have our best-performing Windies players available for selection in these important games."

Their study, published in the journal JAMA Internal Medicine, argued elderly people had the least to gain.
The team at University College London (UCL) has called on doctors to discuss the risks more clearly with patients.
The charity Diabetes UK said doctors needed to strike a careful balance when prescribing treatment.
Type-2 diabetes is an inability to control blood sugar levels and is linked to lifestyle factors including diet and obesity.
In the long-term it is linked to heart disease, kidney damage, nerve damage and even blindness.
Drugs such as metformin can be used to lower blood sugar levels to prevent the side effects.
The report, which was carried out by the University of Michigan as well as UCL, said an average 45-year-old who dropped their blood sugar levels by one percentage point would gain 10 months of healthy life, compared with three weeks for a 75-year-old starting treatment.
It added this needed to be balanced against the down-sides to a lifetime of medication including: Having to have multiple injections and blood sugar tests each day, drugs causing indigestion or sickness, or insulin treatments risking blood sugar levels dropping dangerously low (hypoglycaemia).
One of the report's authors, Prof John Yudkin, told the BBC: "What it means is if you're someone with type-2, it's your right to know what the benefits of the treatment are in terms of gain in life expectancy or reduction in heart attacks or going blind.
"And then you are entitled to decide, but not many doctors have got those figures to hand."
He said GPs were too "target focussed" and were often looking only at the blood sugar level.
The findings do not apply to people with type-1 diabetes.
Commenting on the report, Simon O'Neill, the director for health intelligence at Diabetes UK, said: "Sometimes there is a balance to be struck where certain medications might help give someone a longer life, but also cause side effects that might negatively impact on quality of life.
"This study highlights the importance of looking at the individual needs of the person with type-2 diabetes, rather than adopting a blanket approach."
Patients are advised not to make any decisions without consulting their GP.
The National Institute for Health and Care Excellence, which advises the NHS on medication, said: "The current NICE guidance on the management of type-2 diabetes recognises that glycaemic [sugar] control targets should not impair a person's quality of life as a result of the side effects of treatment.
"Where medication does not help achieve this target level, lifestyle therapies such as dietary advice should be offered."
Refreshed guidelines are due to be published next summer.
Chris Gayle is among the West Indies players who could now play in this year's one-day series in England after a "temporary amnesty" between their union and the team's cricket board.
[NEXT_CONCEPT]
The downsides of taking medication for type-2 diabetes may exceed the benefits for some patients, researchers have advised.