It would be a 28th trophy in four countries for the five-time Ballon d'Or victor, a haul which includes five Champions League, and the Euro 2016 title with Portugal.
Barca have fallen in the quarterfinals in each of the last three seasons, but Valverde said there was no mental barrier among his players.
Leonardo Semplici dogged side also have history against them, as they have beaten Juventus just once in their history, way back in 1957.
Valverde backed his opposite number Ole Gunnar Solskjaer's complaints about the lack of time between games.
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"I don't know if they did or if it was Messi who chose to be quiet", he told RT.
Barcelona will be facing Manchester United in the most crucial second leg of Uefa Champions League on Tuesday.
"For me, Luis is the same as always, which is playing at the high level he always maintains", Valverde said last month after Suarez earned a penalty and set up another goal in a 5-1 win over Lyon in the round of 16.
But SPAL struck back in the second half, with Kevin Bonifazi finding the net before Sergio Floccari scored to ensure the home side took the three points.
Juventus beat SPAL 2-0 in November.
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SPAL is No. 16 out of 20 teams in the Serie A table, and it's now four points out of the relegation zone. "The league is our objective and the Champions (League) would be a dream".
'We are very wary of the spirit that they have.
It was the Italy international's fourth consecutive Serie A match with a goal, and sixth in as many games.
"They all got better as the minutes passed. It's a good sign for Tuesday, as we must be ready and prepare for the potential of extra time too". He leads the club's outfield players in minutes played this season and, in the Spanish league, Pique is setting the pace for his team in blocked shots, balls recovered from opponents, clearances, and winning one-on-one duels for balls in the air.
The early goal should have settled the Catalans into their stride as their dominance of possession was close to 90 percent in the opening stages.
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One of Mr Trump's top aides said last week that the Democrats would "never" see his tax returns. The California Democrat also called on Trump to take down the video.