"Andrew and I have also agreed that we will review the one-day captaincy at the end of the tour. Andrew is extremely comfortable with that."
Strauss has played 78 one-day internationals, scoring two centuries and 14 half centuries in 77 innings at an average of 31.98 and a strike rate of 75.82 runs per 100 balls.
By not naming an interim head coach now, the ECB is buying itself some time to make an appointment before the Ashes series starts in July.
A good performance in the Caribbean from Andy Flower will make the Zimbabwean a strong candidate. But a big name from Australia might be waiting in the wings.
Tom Moody was many people's tip to succeed Duncan Fletcher when Moores took the role in April 2007.
You'd look at any anything, in this day and age you're not going to turn your back on anything
Australia's Tom Moody on the England head coach role
The Australian was a well-regarded coach at Worcestershire, and had a successful stint in charge of Sri Lanka.
Moody, currently working in Western Australia, appeared interested, saying: "You'd look at anything, in this day and age you're not going to turn your back on anything.
"It's a bit like 2007, a similar thing happened. There was no formal approach but I was one of the favourites for the job.
"I've had no formal approach now, and until I do I don't need to consider anything but concentrate on the Perth Warriors."
Flower is widely regarded as the favourite to be England's next permanent head coach.
Warwickshire coach and 2005 Ashes winner Ashley Giles is also in the frame, as are Dav Whatmore and Graham Ford.
England Test squad for tour to West Indies: Andrew Strauss (Middlesex, capt), Tim Ambrose (Warwickshire), James Anderson (Lancashire), Ian Bell (Warwickshire), Stuart Broad (Nottinghamshire), Paul Collingwood (Durham), Alastair Cook (Essex), Andrew Flintoff (Lancashire), Steve Harmison (Durham), Monty Panesar (Northamptonshire), Kevin Pietersen (Hampshire), Matt Prior (Sussex), Adil Rashid (Yorkshire), Owais Shah (Middlesex), Ryan Sidebottom (Nottinghamshire), Graeme Swann (Nottinghamshire).
England one-day squad for tour to West Indies: Andrew Strauss (Middlesex, capt), James Anderson (Lancashire), Ian Bell (Warwickshire), Ravi Bopara (Essex), Stuart Broad (Nottinghamshire), Paul Collingwood (Durham), Steven Davies (Worcestershire), Andrew Flintoff (Lancashire), Steve Harmison (Durham), Dimitri Mascarenhas (Hampshire), Samit Patel (Nottinghamshire), Kevin Pietersen (Hampshire), Matt Prior (Sussex), Owais Shah (Middlesex), Graeme Swann (Nottinghamshire), Ryan Sidebottom (Nottinghamshire).
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