The Italy international has been a rumoured Gunners target for some time, with Arsene Wenger believed to be keen to lure him to the Emirates Stadium amid talk that he is keen to quit the club due to a lack of playing time.
Giovinco made just 17 Serie A starts last term as the Old Lady secured a third successive league title, making a transfer away from Turin look like a possibility.
Liverpool have been alerted by this as Brendan Rodgers plans major moves in the coming months after securing Champions League football at Anfield for 2014/15.
The 27-year-old is seen as a good option to work with Daniel Sturridge, Luis Suarez and Raheem Sterling, with the Northern Irishman aware that he will have to rotate his options to cope with continental football.
Arsene Wenger may also move, but his preferred option appears to be a genuine centre-forward to provide the goals needed for a sustained title push.
£40m Real Madrid man Karim Benzema is a rumoured target.