Morata is expected to leave Real this summer and is pushing for a permanent transfer.
"We are trying to do something for the club and clearly we are interested in Morata," Allofs told WAZ. "It is a difficult task, as clubs like Arsenal, Juventus and Borussia Dortmund are also interested in him."
Juventus have tabled a new bid of €18 million for Morata this week.
For the big stories and the banter follow us on Twitter: @tribalfootball