According to Goal.com, the Blues are battling League One rivals Ipswich for the 20-year-old's signature on loan.
Woodburn spent last season on loan at Oxford United, although he missed a large portion of the season after suffering a broken foot.
He did return to fitness for Karl Robinson's play-off campaign after the season was curtailed amid the Covid-19 outbreak, however.
Woodburn featured in both legs of Oxford's semi-final penalty shootout win over Pompey, as well as coming off the bench in their defeat to Wycombe in the Wembley final.
In total, he registered one goal and five assists in 16 appearances at the Kassam Stadium.
The Wales international is well down the forward pecking order at the Premier League champions, though, and is reportedly set for another loan move.
Woodburn, who is the youngster goalscorer in Anfield history, is supposedly wanted by Pompey, Ipswich and clubs in the Dutch top flight.
The report says: ‘Liverpool will also look to loan Ben Woodburn, with Ipswich and Portsmouth interested in signing the Wales international, who saw a promising spell at Oxford ruined by a broken foot last season.
‘Goal understands Woodburn, 20, also has admirers in the Eredivisie.’
Being only 20 means the Woodburn would be exempt from salary cap restrictions.