According to Mundo Deportivo (h/t Tuttosport via Football Italia), signing Dybala is a "forbidden dream" of Real's—he has also been heavily linked with Barcelona—while Juve are interested in Kovacic.
But the report added Juventus won't accept less than €120 million (£109 million) for Dybala, so Real's success in pursuing the Argentinian could depend on how highly the Italian champions value Croatia international Kovacic.
Real's archrivals Barca have been linked with a £108 million move for Dybala to replace Neymar, who recently departed to Paris Saint-Germain for £200 million, per Corriere dello Sport (via Joe Short in the Express).
Los Blancos would be delighted to steal Dybala from Barca's clutches while, at the same time, snapping up one of the best young attacking talents in Europe.
Dybala, 23, netted 19 goals and provided seven assists in all competitions last term as Juventus won a league-and-cup domestic double and reached the final of the UEFA Champions League, per WhoScored.com.
He boasts all the attributes to be a genuine attacking superstar, including excellent linkup play, fine close-ball control and a fearsome left foot.
Dybala could be an ideal successor for Cristiano Ronaldo at the Santiago Bernabeu, while Kovacic would be no great loss for Real manager Zinedine Zidane.
Kovacic, 23, is a talented playmaking midfielder and commanded a fee of €32 million (£22.5 million) when Real signed him from Inter Milan in 2015.
With Toni Kroos and Luka Modric in the Real squad, however, he faces huge competition to earn a consistent first-team place and was an unused substitute in June's Champions League final.
At Juve, he would likely be granted more minutes by manager Massimiliano Allegri, but it is unclear how much of a temptation he will be in Real's bid to sign Dybala.