3. Sort out the backup for attack
Morata's return from Juventus was sealed by the youngster's good showing in the group stages at Euro 2016. It seems unlikely, though, that Spain's first-choice No. 9, who is 24 in October, will be happy as a backup to the untouchable "BBC" of Karim Benzema, Gareth Bale and Cristiano Ronaldo.
Complicating matters are Benzema's continuing legal issues, with no date yet set for his trial on charges of blackmailing fellow France international Mathieu Valbuena, and there is the possibility he could be unavailable at some point.
Borja Mayoral has been loaned to Wolfsburg and Zidane appears happy for Jese to get playing time elsewhere, but some backup goal-scoring support is needed. Signing an experienced and versatile finisher, who does not expect to play every week, would be ideal -- if not easy to find.
4. Persuade Ronaldo to relax every now and again
As always at Madrid, the main issue for the coach is to get the best out of Ronaldo. The Portuguese, who turns 32 next January, will miss most of preseason -- at least -- due to the knee injury he suffered in the Euro 2016 final. Further, clocking up too many minutes through the autumn and winter leaves him at less than 100 percent for the big games of April and May.
A factor will be the three-time Ballon d'Or winner wanting to remain in the spotlight as he pursues a fourth trophy. Zidane might feel he can do without Ronaldo for Alaves or Espanyol at the Bernabeu, but the player himself will need to be convinced to sit out such opportunities to boost his scoring numbers.
5. Play nicer football
When former galactico Zidane took over from the methodical Benitez in January, there was an expectation that Madrid would suddenly start to play dazzling football. Early games brought some big home wins but, bit by bit, the team became more cautious and reactive, with holding midfielder Casemiro becoming almost as important as Ronaldo or Bale.
There were some grumbles about this attritional football in the spring, although few were worried when the Champions League trophy was lifted in May. Longer term, though, the Bernabeu and Perez would prefer their team to provide more entertainment.