Controller Jeff Ford believes that the hit Fox musical comedy could have been a "great" success for the broadcaster.
Speaking at a Broadcasting Press Guild meeting today, Ford disclosed: "We almost got the first series of Glee. That would have been great for Channel 5."
Meanwhile, Ford also explained why the network decided not to bid for the critically-acclaimed Homeland, which premiered on Channel 4 with over 2 million viewers on Sunday.
"I don't think Homeland would have been right for us," he continued. "It is a very intense show. I want shows that are passionate, honest and relevant."
Dana Delany's Body of Proof is Channel 5's latest US acquisition, recording strong numbers when it premiered in January.
More integrated US shows on Channel 5 include CSI, Law & Order and The Mentalist.