Palace was beaten 1-0 by Chelsea on Sunday, failing to score for the second successive match, and Hodgson's men have now found the net just 17 times across their opening 20 league fixtures.
The former England boss has identified Solanke as a man who could improve the side's fortunes at the top end of the pitch, with a number of other Premier League clubs linked to a January loan move for the 21-year-old.
Solanke has not appeared for Premier League leader Liverpool this season and is behind the likes of Mohamed Salah, Roberto Firmino and Sadio Mane in the pecking order.
"First of all, we’ve got to try and make sure we do get him here on loan," Hodgson told reporters at a news conference.
"If [Palace chief executive] Steve [Parish] has mentioned that, then it's no secret he's a target.
"What would he do? Provide an attacking threat. He's a proven goalscorer through all the age groups at 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."
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