The former Bianconeri striker believes the club's pursuit of continental success will be dependent on them securing the right signings this summer
Vialli was part of the squad that saw the Bianconeri lift their last European Cup in 1996, in a spell in Turin that saw him score 33 times in four years at the club.
Speaking to Tuttosport, the 48-year-old Italian stressed that the Old Lady should focus on Europe after winning back-to-back league titles, but need quality acquisitions if they are to once again become European champions.
"It is normal that after two consecutive championships that, perhaps even subconsciously, attention being shifted to something more important, albeit at the cost of giving up a little bit in the league," the former Chelsea forward said.
"But it all depends on recruitment drive. It is true that they were stopped in the second round only because they met Bayern Munich, but it is equally true that the Champions League presents a higher level of difficulty.
"If the players who Antonio Conte has requested arrive, those who he wants to bet on, then you can really see Juve playing the lead role until the end of the season."
The Bianconeri have been linked with a host of stellar signings of late, including the likes of Stevan Jovetic, Carlos Tevez and Luis Suarez, and Vialli stressed that the lure of the Champions League means that success is worth investing in.
"It is a competition of an unparalleled charm," the ex-Sampdoria man enthused.
"[The Champions league] is beautiful, interesting, unpredictable. But it tremendously difficult."
Juventus won the Serie A title by a clear 10 points last season.