The BBC reported this week that the 25-year-old, who plays for Mexican side Atlas on loan from Lazio, was considering declaring himself available for the Caribbean nation.
Morrison, who played for England as a youth player up to Under-21 level, tweeted on Tuesday to say he hopes to finalize terms with the Jamaican Football Federation in the coming days.
"Making my way to Jamaica," he wrote. "Sorting my documents & papers this week so can be ready for the next games.
"Looking forward to watch the game on Sunday 25th [against Antigua and Barbuda]."
Morrison came through United's academy and was part of the FA Youth Cup-winning side of 2011 that also included Paul Pogba and Jesse Lingard.
He was described by former United and England defender Rio Ferdinand as the best young player he had ever seen, but his early career was blighted by off-field problems.
making my way to Jamaica— ravel morrison (@morrisonravel) March 20, 2018
Sorting my documents & papers this week so can be ready for the next games..
Looking forward to watch the game on Sunday 25th
Jamaica failed to qualify for CONCACAF's final round of World Cup qualifying, but the Reggae Boyz have shown well in the region over recent years, reaching the final of the Gold Cup in both 2015 and 2017.