Origi was handed a rare start against Atalanta BC in the Champions League on Wednesday night, but the 25-year-old struggled to contribute in his team's 2-0 defeat.
A recent report claimed that the forward was open to leaving the Reds during the winter transfer window as he looks to secure a spot in the Belgium squad for next summer's European championships.
Shaqiri, meanwhile, has only made two Premier League appearances this season and is also down the pecking order when it comes to starting roles at Anfield.
According to The Express, Liverpool could look to move both players on at the start of 2021 in order to boost the club's transfer kitty, with a new centre-back thought to be a priority in the winter market.
Jurgen Klopp's side will be looking to make it back-to-back Premier League wins when they travel to Brighton & Hove Albion on Saturday afternoon. body check tags ::