This is according to reports from Italy cited by The Daily Star, which further suggest that the Serie A outfit will only decide on the player's future after this summer's World Cup - seemingly in the hope that a good performance for Ghana during the tournament could perhaps increase his £7 million valuation.
The news that Liverpool are leading the chase for Badu's services is likely to disappoint Arsenal, with the Gunners - along with North London rivals Tottenham - having watched the 23-year-old.
It has been a truly fantastic 2013/4 campaign to date for Liverpool, with Brendan Rodgers' men sitting pretty at the top of the Premier League following Sunday's thrilling 3-2 win over title rivals Manchester City at Anfield.
And while many had only expected them to challenge for Champions League qualification - a feat that has eluded them over recent seasons - it appears that Liverpool now really could be on the cusp of their first top-flight triumph since 1990.
However, despite possessing an impressive squad brimming with world-class attacking talent, Rodgers will know that he must continue to make improvements if his squad are to continue to progress.
They will particularly need to address their obvious defensive weaknesses and the potential signing of the versatile Badu - who is at this best sitting in front of the back four - could certainly help in that regard.
Whether Arsenal - or indeed Newcastle or Italian outfit Napoli, who are two other sides linked with the in-demand Ghanaian - are plotting their own swoop to pip Liverpool to Badu remains unclear.
Arsene Wenger would appear to have more pressing transfer priorities, with the addition of a quality new striker surely top of Arsenal's agenda heading into what is sure to be a typically frantic summer window.