The 33-year-old midfielder, who started his career with Rovers, has been without a team for two years following his departure from Cardiff City in 2011.
"We got a phone call from his agent asking if we'd have a look at him," Moore told the club's official website. "He fell out of love with the game, but he's back in love with it and he wants to come back.
"We said to bring him in and we've got sports science guys working with us now who will monitor his fitness.
"In two or three weeks time when he's fit and can play then who knows what might happen, but at the present time he's here to train and we'll have a look at him."
Koumas signed his first professional deal with Tranmere in 1998 before joining West Bromwich Albion four years later.