"Liza saw him in [different play] Leap of Faith. Also, she does not smoke marijuana. [Liza saw Leap of Faith in] April, 2012, so he's way off."
Odom appeared to pre-empt the comment with a message penned on Twitter on Monday, in which he appeared to explain he was only joking with his comments on the US TV show.
"A.) Liza, I love you. The pot cloud is alleged. B.) Liza, was so kind to me bacjstage (sic) at Leap of Faith. I'll never forget it ever," he wrote.
Apparently the two shared a short conversation in which Minnelli enquired whether Odom had ever seen her perform.
When he admitted he hadn't, she responded: "Then you still have something to look forward to."
The issue of substance abuse is a sensitive one for Minnelli, as the 69-year-old star has spent time in rehab in the past, most recently in March.
In an interview with The Guardian newspaper in 2008, the star opened up about how hard controlling her intake of alcohol had been.
"My whole life, this disease has been rampant," she said. "I inherited it, and it's been horrendous, but I have always asked for help."
The star's mother Judy Garland suffered from her own addictions before overdosing in 1969.
- AAP