Primero descarga Parallels Desktop 12.1.1.41491

Si antes tuviste Parallels instalado, ejecuta en terminal:

sudo rm -rfd ~/library/preferences/com.parallels*
sudo rm -rfd ~/library/preferences/parallels/*
sudo rm -rfd ~/library/preferences/parallels 
sudo -s rm -rfd /private/var/db/parallels/stats/*
sudo -s rm -rfd /private/var/db/parallels/stats 
sudo -s rm -rfd /private/var/db/parallels 
sudo -s rm -rfd /library/logs/parallels.log 
sudo -s rm -rfd /library/preferences/parallels/*
sudo -s rm -rfd /library/preferences/parallels 
sudo -s rm -rfd /private/var/db/parallels 
sudo -s rm -rfd /private/var/.parallels_swap 
sudo -s rm -rfd /private/var/db/receipts/*com.parallels*
sudo -s rm -rfd /private/tmp/qtsingleapp-*-lockfile 
sudo -s rm -rfd /private/tmp/com.apple.installer*/*
sudo -s rm -rfd /private/tmp/com.apple.installer*
sudo -s rm -rfd /private/var/root/library/preferences/com.parallels.desktop.plist 
sudo rm -fr ~/Library/Logs/parallels.log 
sudo rm -fr /Library/Preferences/Parallels/
sudo rm -fr ~/Library/Preferences/Parallels 
sudo rm -fr /private/var/.Parallels_swap 
sudo rm -fr /private/var/db/Parallels/Stats 
sudo rm -fr /private/tmp/qtsingleapp-Parall-c0ce-0-lockfile 
sudo rm -fr ~/Library/Preferences/com.parallels

Si tienes Little Snitch bloquea cualquier petición de parallalels o agrega estas lineas al archivo Host(/etc/hosts/) :

127.0.0.1 registration.parallels.com 
127.0.0.1 parallels.com 
127.0.0.1 update.parallels.com 
127.0.0.1 myparallels.com 
127.0.0.1 pd6.blist.parallels.com 
127.0.0.1 pd7.blist.parallels.com 
127.0.0.1 pdfm7.blist.parallels.com 
127.0.0.1 pdfm7.vl.parallels.com 
127.0.0.1 pdfm7.cepreport.parallels.com 
127.0.0.1 webservices.pdfm8.parallels.com 
127.0.0.1 buka.parallels.com 
127.0.0.1 pdfm8.blist.parallels.com 
127.0.0.1 pdfm8.vl.parallels.com 
127.0.0.1 pdfm8.report.parallels.com 
127.0.0.1 pdfm8.cepreport.parallels.com 
127.0.0.1 download.parallels.com

Finalmente abre Install.app y reinicia.