"It's no secret he's a target," said Hodgson. "What would he do? Provide an attacking threat. He's a proven goalscorer through all the age groups at (former club) Chelsea and England.

"If he comes here, it'll be up to him to show he can do that in Premier League football.

"He's someone with the profile we're looking for, and the ability we are looking for. We know him better from the England games, and the performances with England.

"I thought he was a good signing from Liverpool's point of view, but he's been kept out of the team by some very strong players.

"It would take some player to knock their front three out of the team so it's not a negative in relation to him that he's not been able to do so."

Asked if his team could have been more adventurous against Chelsea, who remain fourth, Hodgson responded: "If we'd have wanted to be beaten 4-0 or 5-0, possibly yes. Chelsea were really very good.

"Our first half was disciplined and focused and we limited their goalscoring chances. We were not able to get the ball from them. But if you open yourselves up, you can see them exploit the space."

Victory increased the gap between Chelsea and fifth-placed Arsenal to five points as the league season enters its second half but came with Olivier Giroud suffering an ankle injury that saw him leave Selhurst Park on crutches.

"(In training) in 10 minutes we had three injuries," said Chelsea boss Maurizio Sarri. "(Cesc) Fabregas, (Ruben) Loftus-Cheek and (Danny) Drinkwater – then Giroud, and we were already without Pedro and (Callum) Hudson-Odoi.

"We are in trouble because, in January, we have to play every three days. Fabregas is a neck problem. The injury was in the last five minutes of training, so I'm not sure whether he has to rest for two or 10 days. I will have a meeting with the doctor.

"For 85 minutes we were in full control (against Palace) without conceding anything to the opponents. I didn't like only that we weren't able to kill off the match before.

"We were better in the second half, because in the first half we did everything very well but too slowly. In the second half, for 40 minutes, we moved the ball better."

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