The deal, if agreed, would mean the United States' most capped international moving to Everton for three months starting in January.
"Landon is a player (manager) David Moyes has identified as someone he would like to bring to the club," Everton chief executive Robert Elstone told the club's website.
"We are working to make that happen and hope we can reach agreement soon with all the appropriate parties."
The Galaxy responded with a statement of their own saying that no decision had been taken over any loan move.
"We are aware of Everton's interest in Landon Donovan, as they are one of a number of clubs who have contacted the Galaxy about the possibility of a short term loan agreement for Landon.
"The Galaxy, MLS and Landon's representative will work together to determine if and whether an arrangement with Everton or any other club will be beneficial to all parties," read the statement.
The 27-year-old, who has played 120 times for the United States and has scored a record 42 goals will be a key member of their team to face England in next year's World Cup finals, helped LA Galaxy to the final of the MLS Cup last month.
LA Galaxy have finished their 2009 campaign which means Donovan, who has played in Europe with Bayern Munich and Bayer Leverkusen, could remain at Everton until mid-March.
Donovan's LA Galaxy team mate David Beckham has already agreed to join AC Milan on loan in January for the second year in succession as he looks to cement his place in the England squad.
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