Domenico Di Carlo and Davide Ballardini are being linked with the Livorno job given the uncertainty over Davide Nicola.
The 40-year-old could be replaced following the 3-0 loss against Chievo which has left them in the relegation zone.
Nicola led the Amaranto to Serie A last season, but the club have won just one of their last 11 in the top flight.
Di Carlo is available after he was sacked at Chievo Verona last term, while Ballardini hasn’t worked since leaving Genoa in the summer.
Former Napoli and Lazio boss Edy Reja has reportedly already rejected the option of taking charge at the Picchi.