It is understood that the two clubs have agreed a season-long loan deal for the 23-year-old England international.
Rodgers said: "Andy Carroll is having a medical at West Ham. The club have made a monumental investment in big Andy and he is not playing at the moment.
"He has made it clear he wants to play and this is a chance for him to do that."
Carroll, who joined the Reds for a club-record fee of £35m in January 2011, has scored six goals in 44 Premier League games during his time at Anfield.