The best scenario he can hope for now is to be available for the second of the two three-day matches that precede the First Test, starting on 11 March, but that might be expecting too much.
Jones did enough form and fitness-wise on the A trip to India to earn promotion to the senior party.
He took 10 wickets on his return to First Class cricket and displayed the pace and reverse swing that first excited the England hierarchy when he burst onto the Test scene in 2002.
If he is ruled out of the tour, potential replacements include Richard Johnson, James Kirtley, Martin Saggers and Sajid Mahmood.
At a time when England's bowlers continue to be hit by fitness worries, it is no surprise that they are employing a woman whose company slogan promises: 'We make your body work for you'. Vickki Byrne, whose working title is 'massage therapist', has been hired for the duration of the 11-week trip in the Caribbean in an attempt to further improve the fitness of England's squad.
The owner of Body Works International, based at Reading, has helped the team at home, on an occasional basis, for the last two years.
But now England have decided they will benefit from having her with them throughout this tour.
'In the past we have hired local people overseas but the problem is that we don't know them very well and they don't know the players or their fitness history,' said England and Wales Cricket Board spokesman Andrew Walpole.
Byrne joins a management team on tour that already includes a physiotherapist and a fitness specialist.
'We will work very closely together,' she said as England immediately got down to business in Kingston today after their 10-hour flight from London. The players began with a session in the swimming pool followed by afternoon nets.
Byrne is no stranger to working with international sports stars, having toured the world as a massage therapist on the ladies' tennis circuit.
Women, especially physios, have become common in English cricket but this is the first time one has been recruited by the full national side to work with them overseas.