The Italian forward has been widely tipped to leave the Yellow Submarines this summer and was expected to join Barcelona before the European champions signed Alexis Sanchez.
Juventus then stole a march on their rivals for the player's signature, and the two sides have been locked in negotiations in recent weeks as both parties attempt to thrash out a deal for the player.
Federico Pastorello, Rossi’s agent, urged Juventus to up their offer for the 24-year-old to £21.8 million, but the Old Lady now believe the Spanish side are unwilling to sell.
“Rossi is a real talent of the Italian game. He is a player who we have put our eyes on, like other clubs,” Juventus director general Giuseppe Marotta told Sky Italia.
“We'll try to sign him, but over the last few hours it has emerged that Villarreal have the intention of keeping him.
“If Rossi doesn't arrive then we'll take a look around.”
Juventus are now tipped to turn their attentions to AS Roma forward Mirko Vucinic as an alternative to Rossi.
Vucinic, who has been linked with a move to Manchester United, Tottenham Hotspur and Blackburn Rovers, wants to leave the Italian capital but Marotta concedes it would be a difficult deal to finalise.
“We do like him, but this is another really difficult operation to conclude,” he added
“We want to complete our squad, to fill the gaps. There is still a month left.
“We are looking for an important objective, but it is not easy as we are not as competitive as the English and Spanish clubs.”
NEWS:Juventus told to improve Rossi bid
'Obviously Messi is the best player in history and being compared to him means that you're doing things right, but I try to be myself': Barcelona star responds to comparisons with Argentine legend
'Darwin Nunez would be gold for Arsenal': Liverpool legend claims Gunners should have signed Uruguayan striker in January
