The Serie A winners are looking to bolster their ranks in the middle of the pitch due to the long-term absence of club icon Claudio Marchisio.
The 30-year-old underwent surgery earlier this year and is expected to be out another six months following a knee injury, leaving Juve short on midfield quality.
Gomes, 22, has impressed at Los Che this season and the Italians are keen to close a deal in the face of interest from the likes of Manchester United. Talks have already opened with the player's agent Jorge Mendes, and the club would be willing to spend up to €30 million on the Portugal international.
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With an approach for Gomes already underway and the repatriation of Mario Lemina from Marseille a done deal, Roma star Pjanic nevertheless remains a tempting figure after his brilliant season in 2015-16.
The Bosnian's release clause at the Stadio Olimpico is worth €38 million, but Goal understands that Bianconeri director Giuseppe Marotta is not considering matching that valuation in order to force a sale.
Any deal made with Juve's Serie A rivals will have to come with Roma's consent, and the champions will attempt to open talks in order to gauge the possibility of taking Pjanic for the coming season.
Daniele Rugani, Simone Zaza and Stefano Sturaro could also be used as make-weights in a cash-plus-player deal to tempt the Giallorossi into releasing their midfield lynchpin, should Marotta wish to cut transfer outlay in what promises to be a busy window at Juventus Stadium.