Everton parted company with Roberto Martinez on Thursday afternoon after a disappointing season that sees them finishing outside of the top ten for the second successive year.
Espanyol have similarly struggled this season, finishing just outside of the relegation zone in La Liga.
That will likely see current manager Constantin Galca leave the club, with them eyeing several potential replacements.
Their prime target appears to be former Chile manager Jorge Sampaoli, but a deal to secure him is difficult, with Lazio a possible destination instead.
That has led Espanyol to draw up a list of other targets, and Roberto Martinez is among them alongside departing Watford boss Quique Sanchez Flores, according to Marca.
They are yet to make an offer for the former Blues boss, and as yet it is unknown how he would view one should it be made.
He is likely to be keen on a stay in England given how long he has been there, but may fancy a return to Spain to repair his somewhat damaged reputation.