L.A. has been making last-ditch efforts to keep Howard on the team, but sources have said that Howard is already looking elsewhere.
Howard is said to favor the Dallas Mavericks and the Houston Rockets.
ESPN analyst Chris Broussard said the main reason for Howard to leave is a clash with head coach Mike D'Antoni's system.
Former Lakers coach Phil Jackson said that he would like to see Howard stay with the team. Jackson does not have any pull over the Lakers save for his relationship with his fiancee, Lakers executive owner Jeanie Buss.
Lakers general manager Mike Kupchak emphasized retaining Howard in a press conference Tuesday.
"He's our future," Kupchak said.
Howard can reach a verbal agreement immediately on July 1, but cannot sign a contract until July 10, the end of the league's annual moratorium.
The Lakers can pay Howard up to $118 million for five years, while other teams can only offer up to $88 million over for years.