Jimenez, 26, was used sparingly by Benfica last season, starting just six times in the league as Rui Vitoria's men romped to the title. The Mexico international featured a further 13 times from the substitutes' bench and managed to score seven times in Liga Nos, and interest in his signature has grown after an impressive Confederations Cup campaign with his country.
West Ham United and Liverpool are both monitoring Jimenez, according to the Daily Mail, and Jimenez's recent comments seem to reveal his desire to ply his trade in the Premier League.
The Benfica hitman rejected West Ham's interest in the summer of 2015 - he missed his medical with the Hammers because he overslept - but Jimenez was keen to stress that he has not 'closed any doors' over a potential move to England.
"The Premier League is a great championship, but you have to wait," Jimenez said. "I don't close any doors and we'll see what happens. I'm still at Benfica. Now, I'm going to have a good vacation then go back to work with everything."
"I saw the news came out but I don't know anything. I was concentrating on the national team. I have a date to return to Benfica, to join the pre-season games and I'm in the club's hands."
Slaven Bilic's men did try to sign Nigerian striker Henry Onyekuru from KAS Eupen earlier this summer, but the talented starlet ended up signing for Everton in a deal worth £7m.
But with the future of Daniel Sturridge far from certain Jurgen Klopp may be poised to delve into the transfer market for another striker, though his immediate focus is on the Reds' pursuit of RB Leipzig's Naby Keita who is believed to be keen on a move to Anfield.