Keane is understood to be interested in a move to the United States, but the agreed deal is complicated by MLS rules, which state that any American team must have only three high-earning squad members, known as "designated players".
The Galaxy currently have David Beckham, Landon Donovan and Juan Pablo Angel registered as their "designated players" and must lose one of them to allow Keane to join.
Angel, the former Aston Villa striker, is the most likely player to leave the Galaxy, with Philadelphia Union reportedly interested in signing him.
Another problem that may hinder the deal is that the MLS transfer deadline passed at midnight EST (5am UK time on Monday).
The Galaxy are yet to make any official announcement on whether the transfer has gone through, but their president Tom Payne said any signings would not be formally announced until Monday evening UK time.
Keane is surplus to requirements at White Hart Lane after dropping down the pecking order over the past two seasons, and has recently stated his desire to leave.
The Republic of Ireland striker, who has had two spells at White Hart Lane, played 13 times for Tottenham last year before being shipped out on loan to West Ham, where he failed to impress.
The 31-year-old made 254 appearances for Spurs during his first spell between 2002 and 2008, during which time he scored 107 goals.
He then moved to Liverpool for ?20million but returned to north London within six months after a torrid time at Anfield.
Redknapp preferred to use Jermain Defoe, Roman Pavlyuchenko and Peter Crouch last season and the arrival of Rafael van der Vaart further reduced Keane's first-team opportunities.
Blackburn and Championship side Leicester are also thought to be interested in the former Inter Milan striker.
However, Leicester boss Sven-Goran Eriksson has already conceded defeat in his attempt to sign Keane.
"I saw in the papers that Robbie Keane is going to play with David Beckham. If that is right, it is difficult to compete," Eriksson told the Leicester Mercury.
"We can compete with Championship clubs but, when a player decides to go to the Premier League or if it is right Keane is going to LA, it is difficult.
"If you are player and you have the chance to play in the Premier League, you understand that is what they want to do.
"Shane Long is an example because he had the chance to go to a good Premier League club. It is not about money."
Source: Team Talk
Source: Team Talk