The 33-year-old is expected to leave the Spanish side in the current transfer window after new coach Ronald Koeman decided the attacker had no place in his plans for the future.
Juventus emerged as the favourites to land him and the Uruguay international even reached an agreement with the Serie A champions over a €10 million (£9m/$12m) contract, and subsequently travelled to Italy for a language exam in order to get a passport.
But Juve grew pessimistic over their hopes of getting a deal over the line and new coach Andrea Pirlo recently admitted that the move looked unlikely due to bureaucratic issues over securing a passport.
The Bianconeri have now decided to put an end to their efforts and look for other options in attack before they need to inform UEFA of their squad for the Champions League.
“Suarez can be removed from that list, because the time it takes to get the passport is longer than the transfer deadline or the moment we can hand in the Champions League lists," Paratici told Sky Sport.
“We evaluated the Suarez option when it was proposed to us. He was in the process of getting Italian citizenship, so we evaluated the possibility of registering him in time.
“It is not possible, so he was never really close.”
Paratici says 34-year-old Dzeko is not the only option they are considering and says they will not rush to make a signing.
“Let’s say there isn’t a Dzeko situation, it’s a striker situation, as Juventus need a centre-forward. Right now we are only thinking of one striker, not two," he said.
"We know what we want and are working towards that calmly, there are 15 days to go in the transfer window and we’re in no rush.
“There are other options, not just Dzeko.”
Goal reported this week that Juventus are looking to bring Moise Kean back to the club after the striker endured a difficult first season with Everton.