The eight-time Spain international has impressed over two seasons in Serie A after leaving the Liga giants in mid-2014.
However, the deal was done with a buy-back clause that Madrid could activate, a move that will reportedly cost them €30million.
Juve general manager Giuseppe Marotta wants Morata's future decided one way or another as the Serie A giants look ahead.
"Our intention is to do things fast with Real Madrid because we plan right away for next season," he said, as quoted by AS.
While Juve are on the verge of sealing a fifth-straight Serie A title, Madrid are fighting for La Liga and remain in the Champions League.
Marotta added that the busy fixture list means he is unwilling to rush the Spanish club into doing a deal over the coming weeks.
"The truth is we now have important objectives to focus upon," he said.
Morata, 23, scored eight league goals in 2014-15 and has six more this season.