Radcliffe, who plays J. Pierrepont Finch in the revival of the musical in New York, isn't the first charismatic actor to take on the role, the New York Post reported Sunday.
"I used to sneak out the back door some nights," Morse, who won a Tony for best actor in the play, and then starred in the 1967 movie rendition. "But Daniel Radcliffe will probably have to sneak out a window."
Morse stars as Bert Cooper, the eccentric senior partner of advertising agency Sterling Cooper Draper Pryce, on the TV show "Mad Men," the Post said.
The role is a nod to Morse's character in the Broadway musical.
In the musical, Finch starts out as a window washer and climbs his way to become chairman of the board of the play's advertising firm.
Mad Men satirizes the world of advertising.
"I know that Matthew Weiner ('Mad Men' writer and producer) wanted me for the role because he remembered me in 'How to Succeed,'" Morse said.
"When I saw the rows of desks and typewriters and everything else from that period, I started walking up and down the aisles singing songs from 'How to Succeed.' You can't believe how similar it is.
"I am so happy for this production. It fills me with joy that they are doing it, and I think Radcliffe is an amazing talent. I know when I see it I will look at the stage and say to myself, 'How the hell did I ever do that?' and tears will probably roll down my face."