The men may have been joined by another three players, though this has not been confirmed.
According to TMZ, the gentleman's club presents itself as a spa and staff have been instructed to give callers that line.
The only indication of the shop's true purpose is when callers are told that it is for men only, and stocks a full bar.
The basketball team say the players took staff at their word and didn't realise what they were walking into until they arrived.
A source told TMZ: "They realised it wasn't the right place for them and immediately left."
However, images from inside the club show Jordan hanging out by the bar, while Cousins stands with a girl who appears to have her arms wrapped around his waist.
Sources from the club say that the men bought some drinks while inside, but nothing else.
The basketball players certainly seem to have been enjoying themselves since arriving in Rio, staying on a cruise ship they have hired after shunning the athlete's village accommodation.
USA Basketball and their sponsor, Cisco, have rented out the entire Silver Cloud cruise ship, to provide enhanced security to such world-famous players as Anthony and Kevin Durant.