The 7-1 loss to Atalanta on Sunday evening was shocking, but partially excused by the fact they were down to 10 men for an hour.
However, on Wednesday night they incredibly lost 4-0 at home against a Roma side that had Federico Fazio very harshly sent off just 32 minutes in.
According to Sky Sport Italia, Tuttomercatoweb, La Gazzetta dello Sport and others, Udinese directors are taking a few hours to think about the various alternatives.
Gattuso is believed to be the favourite, especially as he was in the stands for the 7-1 defeat to Atalanta, alongside his long-term assistant manager.
The former Milan coach has already turned down offers from Genoa and Sampdoria this month, so there is no guarantee he’d accept Udinese.