A fee has been agreed with the Swans and the 30-year-old, having played under Martinez at the Liberty Stadium last season, is unlikely to have any problems agreeing personal terms.
The only delay in the transfer going through may be down to issues surrounding the Trinidad and Tobago international's work permit.
"The player has been given official permission to speak with Latics and he has been in Wigan to undergo a medical and discuss personal terms," said a Wigan statement.
"However, the transfer is far from complete and the player will not be unveiled until the situation over his permission to work in this country is resolved, and this could take some time.
"The club cannot comment any further on the transfer until he is officially registered and confirmed as a Wigan player."