A host of Championship clubs including Leeds United, Norwich City and Preston North End fancy snapping him up for the rest of the season.
Jurgen Klopp will let Woodburn leave Anfield on loan in a bid to get him playing regular football.
And, according to the Daily Mail, the 18-year-old wants to link up with former Wales boss Chris Coleman at the Stadium of Light.
Coleman handed Woodburn his international debut in September.
Woodburn hit a stunning goal against Austria on his maiden appearance for Wales.
Coleman has no money to spend in the January transfer window so is having to look towards the loan market to strengthen his squad.
Woodburn made his breakthrough at Liverpool last season, making nine appearances.
But he has struggled for minutes this term, featuring just once in the EFL Cup.