Ibrahimovic has also been linked with a return to Manchester United, with Ole Gunnar Solskjaer determined to sign a new striker in the January transfer window.
But former Chelsea midfielder Craig Burley believes the Swede should be targeted by Liverpool, as he could provide Jurgen Klopp another option up top.
The Reds are top of the Premier League, and are believed to be looking for backup for Roberto Firmino in the central striker position.
And Burley believes Ibrahimovic would be the perfect option to be brought in for half a season.
Zlatan Ibrahimovic will leave LA Galaxy in January (Image: GETTY)
“We laughed when we talked about if Jurgen Klopp had been asked about him,” Burley explained on ESPN FC. “But this is something I genuinely believe can work short-term.
“I know he doesn’t fit their style, with the pressing style and all that.
“But they have nobody else, literally nobody else, either than Roberto Firmino [in a central attacking role].
“Please don’t talk to me about Divock Origi, you’re talking about Liverpool trying to get over the line in the Premier League for 20-odd years. Sometimes you need something different.
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Craig Burley claimed Zlatan Ibrahimovic would be a backup for Roberto Firmino (Image: GETTY)
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“We’re talking about a guy who may only be coming off the bench now and again for 20 minutes or half an hour, and just bringing something different, that bit of quality.
“Nobody is asking him to run around or close teams down in the first half of a game.
“But I think he can really offer something to a team like that for six months towards the end of the season.
“I don’t suggest it’ll happen, but it would work.”