Jimenez became Benfica's record signing when they paid Atletico Madrid £18.9m for his signature in 2015, but he has only scored 23 goals in 77 appearances in Portugal.
Last season, the 26-year-old made just eight starts in all competitions for his club, but he featured twice for Mexico during the Confederations Cup.
According to A Bola, Jimenez has been put up for sale and that has led to interest coming from the Premier League with just five weeks remaining until the start of the season.
It has been claimed that West Ham - who have previously made an approach for Jimenez - are among the frontrunners as they continue to look for strikers ahead of next season.
Liverpool could also be in the running, with the future of Daniel Sturridge still uncertain after another injury-hit campaign at Anfield.