The Brazil international was a target for both Spurs and Arsenal over the summer, but the Gunners eventually opted for Mesut Ozil while Tottenham signed Christian Eriksen from Ajax.
Hernanes was identified as a potential cut-price target, with his contract set to expire in the summer of 2015.
The report claims Lazio are resigned to losing him then, with the player so far yet to agree a new deal. Arsenal and Spurs are believed to be tracking the midfielder, but face a battle with Atletico Madrid.
The Spanish club have reportedly made an enquiry for Hernanes ahead of a possible January bid. Atletico hope Lazio will be keen to offload the 28-year-old this winter - the last window the Serie A club can command a big fee for their star player.
Next summer, Hernanes will have just a year left on his Lazio contract, forcing the Italians to consider selling him on the cheap or risk losing him for nothing.
Atletico's interest could prompt action in north London, with Arsenal and Tottenham monitoring developments.
Both Ozil and Eriksen enjoyed impressive debuts, but Hernanes could be looked at as another option in a deeper midfield role.
Arsenal, in particular, may be interested with their midfield suffering from several injuries already this campaign.