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The uncapped left-arm seam duo of Gloucestershire's David Payne and Sussex's George Garton also make the cut, but there is no room for Lancashire leg-spinner Matt Parkinson.
The squad features no players currently on Ashes duty in Australia, with the two tours overlapping. The Fifth Ashes Test is due to begin in Hobart on January 14, while England’s first T20 in the Caribbean is on January 22.
Assistant Paul Collingwood will stand in for Chris Silverwood as England's head coach in the West Indies, having flown home from Australia last month after travelling straight there from the T20 World Cup.
“We have selected a strong squad with some serious batting power and a balanced attack as we begin preparations ahead of the T20 World Cup in Australia," Collingwood said.
“The World Cup is less than a year away and there will be increased opportunities for the squad in the absence of those players who are with the Ashes squad.
“I have good memories winning a World Cup in Barbados and I’m really looking forward to going back there with this squad to face a very good West Indies who will test all aspects of our skills.”
England squad for West Indies T20 series
Eoin Morgan (Middlesex – captain), Moeen Ali (Worcestershire), Tom Banton (Somerset), Sam Billings (Kent), Liam Dawson (Hampshire), George Garton (Sussex), Chris Jordan (Surrey), Liam Livingstone (Lancashire), Saqib Mahmood (Lancashire), Tymal Mills (Sussex), David Payne (Gloucestershire), Adil Rashid (Yorkshire), Jason Roy (Surrey), Phil Salt (Lancashire), Reece Topley (Surrey), James Vince (Hampshire).