The 23-year-old is expected to leave his Catalan club ahead of the 2020-21 campaign following their relegation to the second tier of Spanish football.
A number of clubs, including Bayern Munich, have been credited with an interest in the former Spain Under-21 international, who is thought to have a €40m (£35.8m) release clause in his current deal at the RCDE Stadium.
However, according to La Razon, Arsenal are leading the race to sign the central midfielder during this summer's transfer window.
Roca has scored twice and provided one assist in 33 La Liga appearances this season but his efforts have not been enough to prevent Espanyol from dropping into the Segunda Division.
Everton are also believed to be considering an approach in the upcoming market.