The 19-year-old joined Barcelona from Atheltic Paranaense in January after registering 28 goals and 11 assists in 81 competitive appearances for the Brazilian.
The striker struggled to force his way into the side last season, starting just two of his 14 La Liga appearances under Xavi.
While there has been a change in manager, Roque's situation has not improved since the arrival of former Germany boss Hansi Flick.
Roque has not been registered for La Liga and was subsequently omitted from the matchday squad for Saturday's 2-1 win over Valencia at Mestalla.
Everton in pole position for Roque
Barcelona are seemingly ready to part ways with Roque just seven months after signing him for an initial €30m (£25.6m).
According to Spanish outlet Marca, Everton are currently best-placed to sign Roque before the summer transfer deadline.
The Toffees are believed to be leading a number of Spanish teams in the race, including Real Betis, Real Sociedad and Girona.
The report claims that Betis are looking into the prospect of negotiating a loan deal with an option to buy, but they are also considering a number of other targets, including Kevin Denkey and Youssoufa Moukoko.
Everton looking to strengthen forward options
Everton are keen to strengthen in the final third after finishing the 2023-24 Premier League campaign as the second-lowest scorer with 40 goals.
Dominic Calvert-Lewin is Everton's current first-choice striker, but he has been linked with a potential move away from Goodison Park.
Sean Dyche's alternative options to Calvert-Lewin are currently Iliman Ndiaye, Chermiti, Beto and Neal Maupay.
However, it remains to be seen whether Beto and Maupay will still be with the Merseyside club when the transfer window shuts on August 30.