Rangers' manager Walter Smith told The Times that former Rangers player Mo Johnston, Toronto's general manager, had recommended Beasley:
"We had asked Maurice Johnston if he thought there were any players in the American league whom he thought would do well, and he recommended two or three players. The clubs don't own the players over there so the MLS are happy to let him go. We are in the final stages of tying everything up, but we still have to apply for the work permit. He is only 22 and has played the last number of internationals, so I'd hope we will get him."
Edu, who attended last weekend's Rangers' game against Hearts, would join fellow American DaMarcus Beasley at Rangers.
"I think he's worth that amount," Beasley, who joined Rangers in June 2007, told The Times. "Obviously if Walter Smith thinks he's worth that then he is. The manager has a good eye for talent - Maurice will prove that."
Edu, the son of Nigerian immigrants, played three seasons at the University of Maryland, winning the 2005 NCAA title.
He was MLS's Rookie of the Year with FC Toronto in 2007 and has played in 37 MLS games, scoring five goals and notching two assists.
Edu, who has made seven appearances for the USA's full national team, is on the USA's roster for Wednesday's World Cup qualifier against Guatemala.
American Claudio Reyna played for Rangers in 1999-2001.