Greene has a salary cap hit of $2.95 million, while Mitchell's cap hit is $3.5 million.
Both players are expected to receive raises, with the cap expected to climb up around $68 million to $70 million next season.
Greene, 30, and Mitchell, 36, want to stay in Los Angeles, and Elliotte Friedman of CBC first reported that some preliminary talks have started with Greene.
Lombardi is also looking to bringing in a second-line scoring left wing, but the team's backed up against the salary cap and might not be able to make an impact move just yet.
One option the Kings have is calling up Tyler Toffoli or Tanner Pearson from the AHL, but they would need to send someone down, presumably defenseman Keaton Ellerby, who would be subject to waivers.
The Kings are thin on the left side, and which could give Pearson an edge, despite playing in just one NHL game during last season's playoffs.