Hiddink is currently in his second spell as interim manager of the Blues and is set to exit the club at the end of the 2015-16 season, leaving Chelsea searching for a permanent replacement.
And the Southampton manager wants that replacement to be him, declaring in an interview with Dutch radio station Radio 538: "If Guus puts a good word in for me, that would be a big influence."
Koeman, who took over from Mauricio Pochettino at Southampton, has previously managed Ajax, Benfica and Valencia and suggested that he sees his future at one of Europe's elite clubs.
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"I always want to achieve the highest possible level," he added. "That has happened in Holland and that’s what I’d really like to achieve abroad.
"It is certainly something that I always have at the back of my mind."
Southampton, who face Manchester United on Saturday, sit 10th in the Premier League and Koeman has earned praise for his restructuring of the squad following the departures of a number of key players.
But the 52-year-old, who was part of Barcelona's 'Dream Team' as a player, may face competition for the Chelsea job from the likes of Diego Simeone and Massimiliano Allegri, who have both been linked with the post in recent weeks.