They both loved cats.
As of yesterday, over 3,000 Hemingway documents from the Hemingway Museum at Finca Vigia in Havana (read more here) are available digitally to researchers and fans.
It got me wondering if the two ever corresponded. According to Gerald Nicosia, in Memory Babe: A Critical Biography of Jack Kerouac (1994), they did meet in late 1943:
At one cocktail party in the Village Jack met Ernest Hemingway. After addressing him as "Papa," Jack proved too tongue-tied to make much of an impression on his formal idol (p. 112).
Perhaps a letter ensued?
There is a fee for accessing the Hemingway archives, but I'm going to look into it. You never know . . . .