Mr. Cimoszewicz, of the ruling Democratic Left Alliance, has remained untouched by a string of scandals that have tarnished his party. Polls have put him ahead of other hopefuls, including leading conservative Lech Kaczynski.
Poland's President Alexander Kwasniewski cannot run for re-election because he has already served two terms.
Opinion polls indicate Polish leftists will be defeated in parliamentary elections, scheduled for September 25.
Some information for this report provided by AP and Reuters.