The Leeds United striker netted 19 goals in the Championship last season as Leeds fell short of a play-off spot.
A former team-mate of Angel Rangel at Terrassa, the Argentine is a wanted man with a host of Premier League clubs credited with an interest.
The Sun and the Daily Star both suggest that Brendan Rodgers is ready to make Becchio his second big money swoop of the summer after landing Danny Graham for a club record £3.5m fee.
Rodgers is understood to still be in the market for another forward with Barcelona B's Jonathan Soriano and Eidur Gudjonssen linked in the papers over the past weeks.