"We're wonderful. We're unbreakable," the 33-year-old NBA basketball player toldUs Weekly.
"That's why I wear my wedding ring. It is a beautiful ring," he added. "From a beautiful wife."
Odom also told the magazine he's "good" following months of reports he's addicted to drugs and had cheated on Kardashian.
Kardashian also seemed to allude to her love life on Instagram on Thursday.
"In the end, only three things matter: how much you loved, how gently you lived, and how gracefully you let go of things not meant for you," she wrote.
Kardashian, 29, and Odom, 33, reportedly both attended Kanye West's concert at the Staples Center in Los Angeles on Monday, but according to TMZ sources, the hangout session wasn't indicative they're reconciling or getting back together. The concert was the pair's first public outing in months.