Keane, 31, this week revealed he expects to leave Tottenham before the transfer window closes at the end of August.
Widespread reports have claimed the Galaxy want to bring Keane to Major League Soccer, where he could team up with former England captain David Beckham.
The Republic of Ireland's all-time record goalscorer began his career with Wolves and has also had spells with Coventry, Inter Milan Leeds, Liverpool and loans with Celtic and West Ham.
Asked specifically to comment on the Keane link, a spokesman for the Galaxy said in a statement: "We are always looking to improve our squad and have contacted or been contacted by a host of players during the current transfer window.
"As soon as we have something confirmed in regards to any potential player acquisitions we will be sure to alert everyone."