Gerald Ford, April 1942 seems the best answer. The caption says that Phyllis Brown was the model for the girl in picture and that Gerald Ford was the man.
Ford did some work as a model and was not famous at the time.
The related link below shows the cover and contains a quote from the Gerald Ford library where they say they cannot confirm or deny that it is him.
I think it's Katy Perry.
Richard Nixon holds the record for appearing on the cover of Time magazine the most, with a total of 55 covers during his presidency.
Kristin Cavallari appeared on the cover of "Maxim" magazine in October 2005.
If you don't count skyboxes or commemorative issues, Barack Obama has appeared on 25 Time magazine covers through September 2012.
Elizabeth Taylor appeared on the cover of Life magazine a total of 14 times.
The members of the Beatles have been on the cover of Rolling Stone the most times. Either as a group or as individuals, they have been on more than thirty covers. The Rolling Stones, ironically, come in a distant second.
Time Magazine declared President Nasheed a 'Hero of the Environment'. In April 2010?
"Time Magazine's ""The Man of the Year"" cover issue began in 1927. They issue a winner every year and this has lasted every year. Therefore there has been about 83-84 people who have appeared on the cover of Time Magazine."
Franklin Roosevelt
The cast of The Girl on the Magazine Cover - 1940 includes: Millard Mitchell as Photographer
Juliana Daniell appears on the June 2013 cover of Prevention magazine. She has appeared on the magazine a couple of times before.
The sites of popular fashion magazines will often have cover pictures and articles of models and celebrities. Such magazines include Vogue, Fashion Magazine, ELLE, Glamour Magazine, and Cosmopolitan.