Mendes been accused of raping a Brazilian woman in March, the New Zealand Herald and other outlets have reported.
The 36-year-old winger has guided the tiny African country to the round of 32 at the World Cup. Cape Verde will face defending champions Argentina on Friday in Miami.
The alleged victim had been hired to work with the team during a FIFA Series event. She reportedly told authorities Mendes forced his way into her room before sexually assaulting her.
Mendes has not been charged with any crimes.
New Zealand police have confirmed that an investigation is ongoing. The Cape Verde football federation did not respond to requests for comment from The Athletic.
A FIFA spokesperson released a statement to The Athletic about the allegations against Mendes.
"FIFA takes any allegation of misconduct extremely seriously and has a clear process in place for anyone in football who wants to report an incident," read the statement.
"As a general rule, please understand that the independent judicial bodies do not comment on allegations they may or may not have received, or whether or not investigations are underway into alleged cases. Any information they may like to share will be communicated at their discretion.
"FIFA is in contact with the New Zealand authorities. Please understand we cannot comment further at this stage."
Mendes started each of Cape Verde's three matches in the group stage at the World Cup. He is the nation's all-time leader in caps (101) and goals (22).
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