The Italians hope 30-year-old Denmark international Poulsen will fit the bill on Merseyside as the Reds look to replace Javier Mascherano.
Juve are mulling an offer worth £4million plus the holding midfielder for Agger as they step up attempts to land a centre half.
Fancy doing a swap? Juventus are keen on Daniel Agger (left) and may offer Christian Poulsen (right) in exchange
Plans to sign Nicolas Burdisso from Inter Milan look dead in the water as the Argentina international would prefer to join Roma, where he spent last season on loan, if a departure from the San Siro is inevitable.
Mascherano is keen to join former Reds boss Rafa Benitez at Inter Milan and would command a fee in excess of £20m.
At the wheel: Daniel Agger leaving Liverpool's training ground on Monday
Although Poulsen may be tempting as a replacement, Hodgson is unlikely to want to lose a defender without adequate replacement.
The Anfield boss presently has no senior left back at the club and Agger has be known to fill in at that position.
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