Odom was hospitalised on Tuesday, October 13 after being found unconscious in a brothel near Las Vegas and he is considered to be in a critical condition.
According to the Nye County Sheriff's Office, Odom was found unresponsive at Dennis Hof's Love Ranch South in Nevada.
Beckham on Thursday, October 15 took to his Instagram to share a good well message for the former LA Lakers player.
"Stay strong brother," Beckham wrote beside a picture of the former LA Lakers basketball star.
David became familar with Odom during his star in America playing for MLS side, LAGalaxy.
While playing for the LA based's MLS side, Beckham became a supporter of the LA Lakers, with whom Lamar won back to back NBA titles in 2009 and 2010.
Other sports stars have also sent their prayers to Odom.
Dwyane Wade of MiamiHeat wrote: "I pray ths morning for my brother. Dear God he's one of the good ones. PLEASE watch over him and listen to his heart speak #PrayersForLamar.'
"Prayers go out to Lamar Odom, he's been through a lot, an incredible person, praying for you bro, just fight another battle. #QueensBoys," Charlie Villanueva of DallasMavericks wrote.
Former Lakers teammate Trevor Ariza was seen paying Odom a visit at the hospital.
Watch this Lamar Odom video, below: