Marlon Samuels joined up with the West Indies squad in England on Tuesday as the tourists moved close to having their full strength party available for selection.
Samuels linked up with his international team-mates following a stint in the Indian Premier League and the West Indies hope Guyanese duo Assad Fudadin and Narsingh Deonarine, who have been awaiting their visas in Jamaica, will be arriving shortly.
But the duo are unlikely to arrive in time for the West Indies' second and final warm-up match, a four-day fixture against the England Lions starting at Northampton on Thursday.
The tourists risk going into next week's first Test against England at Lord's under-prepared after rain meant only 34 overs were possible in their opening warm-up match, a scheduled three-day game, against Sussex at Hove concluded on Monday.
"Marlon Samuels arrived in the country this (Tuesday) morning and has joined up with the team," a West Indies spokesman said.
"The other two players are still awaiting their visa but we are hopeful that they will be able to pick them up today.
"Until they have those visas in their hand we can not be sure, of course.
"Only when they they get those then we can make the necessary arrangements for them to arrive in England, but we hope and expect that they will be here for the England Lions game.
"Whether any of the players are selected is a matter for the team management to decide," he added.
Although there was desperately little play in their match against Sussex, there as still enough time for West Indies' star batsman Shivnarine Chanderpaul to suffer a finger injury while batting although he was able to continue his innings Monday.
Fast bowler Fidel Edwards remains more of a fitness doubt as he has been sidelined since missing last month's third Test against Australia with a back "niggle".