Jurgen Klopp is shuffling his squad this month as he looks to maintain a title push.
The Reds received £19m for Dominic Solanke from Bournemouth last week.
But according to the Liverpool Echo, Klopp is now wary of weakening his squad further.
The Belgium international isn’t short of suitors.
It’s suggested Wolves, West Ham and Fulham are all vying for his signature.
Despite Klopp’s growing reluctance to sanction his departure, Origi has been a peripheral figure for the Merseyside heavyweights in recent months.
He spent the previous campaign of loan at Wolfsburg and has barely featured this season.
Fulham boss Claudio Ranieri – who is desperately trying to save the Cottagers from relegation – fancies Origi.
The Hammers are also sniffing around with Marko Arnautovic angling for an exit at the London Stadium.
Arnautovic has a big-money offer on the table from an unnamed Chinese club.
Wolves are similarly eager to add firepower to their ranks.
Origi has been earmarked as an alternative option to Chelsea attacker Tammy Abraham.
The highly rated striker is currently on loan at Championship big hitters Aston Villa.
However, rumours had been rife that he could be Molineux bound.
Abraham, 21, currently pockets around £42,500 a week at Chelsea.
Wolves were weighing up a deal that would see him treble his wages.
Sky Sports reporter Rob Dorsett says the saga isn’t necessarily over yet.
He said: “There are reports today that Crystal Palace are keen on signing Tammy Abraham this window but it’s our understanding he will stay on loan at Aston Villa until the rest of the season – unless a big money offer comes in from elsewhere which tempts Chelsea into action.
“Abraham turned down the chance to switch his loan from Villa to Wolves yesterday.
“He’s staying in the Championship rather than the Premier League.”