"Talks have also begun with another player who does not have term for next (season) and that's Andreas Athanasiou," Sportsnet's Elliotte Friedman reported on a bonus edition of "Saturday Headlines."
Friedman added: "The Kings are looking to see if there's a fit (and) they can keep him beyond this year as well."
Athanasiou is a pending restricted free agent currently on a one-year, $1.2-million pact he inked with Los Angeles in December. He's eligible for arbitration if the two sides are unable to agree on a new deal.
The 26-year-old entered Saturday's action with eight goals and seven assists in 31 games. The Detroit Red Wings traded him to the Edmonton Oilers at last year's deadline.
The Kings have reportedly begun to take calls from other teams about Iafallo, who's a pending UFA carrying a $2.42-million cap hit. However, Los Angeles is also discussing an extension with him.