Speaking from Hong Kong, where Juventus are due to play Chelsea in a friendly, Spalletti addressed his relationship with football director Giovanni Carnevali and sporting director Frederic Massara, praising the transfer business done so far this summer.
"I know the quality of the directors because I've known them for a long time," he said. "Up to this point they've shown us the quality of their work, so I have full trust.
"They know, and we know, because we have a good relationship, that there are a couple of situations to complete, and they stayed at home precisely for that, to make the most of any market opportunities that come up."
The clearest of those situations is the goalkeeper position, Juventus's absolute priority at this stage of the window. With a move for Emiliano Martinez having fallen through, a deal for Parma's Zion Suzuki is complicated by strong competition from Paris Saint-Germain, leaving Vicario's move from Tottenham as the option still standing.
Spalletti is understood to rate Suzuki more highly for his footwork and distribution, but has reportedly questioned why Tottenham are willing to let Vicario leave, a factor giving Juventus's hierarchy pause even as they keep the loan-with-option-to-buy structure on the table.
Less advanced is the club's interest in Bologna's Jhon Lucumi, while Juventus are also working to trim their midfield to free up room for further reinforcements there, with Nico Gonzalez a subject of interest from Inter Milan as a possible departure.
Juventus are also keeping a close eye on PAOK playmaker Giannis Konstantelias, according to Sky Sport, with Borussia Dortmund and Chelsea also credited with interest in the Greek forward.
Dortmund remain favourites to sign him, given their track record of investing in young prospects and a squad that already includes several talented teenagers, but Juventus have moved to challenge that position, having watched Konstantelias in action on several occasions.
The Bianconeri have already strengthened that area of the pitch this summer with the arrival of Kerim Alajbegovic, filling the available slots for now, meaning any Konstantelias deal would likely be pursued with an eye on the future rather than an immediate first-team need.
The 21-year-old closed last season with seven goals and three assists in 18 appearances for PAOK, standing out in particular during a Europa League play-off round win over Dynamo Kyiv, in which he scored three goals and provided an assist across the two legs.