Oddo took over in November and oversaw victories in his first five games, but results since then have been unimpressive, losing the last 11.
The club from Friuli-Venezia Giulia lost to relegation strugglers Crotone at the weekend and now find themselves 15th in the table.
Igor Tudov, the former Juventus defender, is the favourite to take over.
The former Croatia international began managing in his home country but has also taken on roles in Greece and Turkey.