Striker Morata has been heavily linked with a move to Premier League club Arsenal this afternoon and Spanish publication AS suggest that Real will ramp up their efforts to sign the €60 million-rated Suarez if he does secure a switch away from the Santiago Bernabeu.
Real Madrid have long been linked with Suarez, the Uruguayan international whose absolutely sensational form for Liverpool during the 2013/14 campaign almost carried the club to their first title success in over two decades and also saw him deservedly announced as the PFA Player of the Year.
Such a saga - that stretches all the way back to last summer when Suarez seemed intent on leaving Anfield - has had its fair share of twist and turns, with recent reports speculating that he has already informed his teammates that he wants to win the title with Liverpool.
Reds fans will presumably be more confident of retaining Suarez's services now than they were at this time last year, chiefly due to the fact that his obvious desire to play in the Champions League will be satisfied after Liverpool automatically qualified for the prestigious tournament thanks to their second-place league finish.
The size and sheer reputation of Real Madrid could surely still hold an appeal for Suarez, however, particularly after Carlo Ancelotti's squad proved their formidable ability by comfortably beating rivals Atletico to lift their 10th Champions League crown on Saturday night.
Replacing Morata with Suarez would certainly represent a significant upgrade for Real. Although the 21-year-old Spaniard has shown several glimpses of real potential, he is not currently comparable to the former Ajax man.
What that potential move would mean for the future of Karim Benzema - Real Madrid's current first-choice striker - is not clear, although it has to be considered unlikely that he would be content with a place on the substitutes bench.