The Maroon 5 frontman, 33, and Glee star, 34, are recording a cover of "Luck Be a Lady," the source tells Us. The song was written by Frank Loesser in 1950, and was featured in the musical Guys and Dolls. It also became one of Frank Sinatra's signature hits.
The new track will appear on Morrison's upcoming album, which is under Levine's label, 222 Records.
"Starting my own label has been a long time goal of mine and I am thrilled to be at the point in my career where it is finally happening," the "Moves Like Jagger" singer said in a statement earlier this month. "I am excited for everyone to hear Matthew's forthcoming album. Great things are in store for him with this release."
And Morrison, who previously released a self-titled album in May 2011 with Mercury Records, was happy to sign on. "Adam and I share the same vision as we begin working on my record together," he said in a statement.
The two hunks have been pals for a few years. "Matthew wanted to make a Broadway standards record," the source tells Us of Morrison, who starred in many Broadway shows before landing Glee. "And Adam loves classic records."