Toffees boss Ronald Koeman went on a mammoth summer spending spree, but has failed to replace the goals of Romelu Lukaku, and another striker still remains high on his wanted list.
Everton have long been linked with a move for Jimenez, and some reports have suggested that Koeman failed with a last-ditch attempt to sign him before the closure of the summer transfer window.
The Portuguese press now claim that Everton will make another move for the Mexican international forward in January, and Benfica could be open to a deal.
Everton's lack of goals is a big concern for Koeman as his side have got the season off to a disappointing start, but it remains to be seen whether Jimenez would be the solution as he lacks Premier League experience.