Wiegman led the Lionesses to the World Cup Final, while Hayes side retained their WSL title.
Spain’s World Cup winning boss Jonatan Giraldez completes the list.
Pep Guardiola is among the nominees for the men’s award after leading Manchester City to the treble.
Inter Milan’s Simone Inzaghi and Luciano Spalletti of Napoli are also on the short list.