The Coronavirus pandemic has led to the postponement of major leagues across Europe and there are fears the European championships which is supposed to run from 12 June to 12 July will be pushed back by a year.
Aside the major leagues, the UEFA Champions League, Europa League and EURO 2020 playoffs have all been suspended.
Several Serie A players have tested positive for the virus including Juventus’ Daniele Rugani, Manolo Gabbiadini and Patrick Cutrone.
A video conference featuring delegates from UEFA’s 55-member associations will be held on Tuesday to discuss the way forward.
"We will try to reach the end of this [Serie A] season because it is fair and correct to have an outcome for the many efforts and sacrifices from our clubs," Gravina told Mediaset on Sunday.
"The hope is that this happens by June 30, without forgetting that in addition to Serie A there are other championships that must be resolved, and we must also include the Champions League and the Europa League. The deadline is June 30, eventually we will see if we have to go beyond."
Regarding European competition, Gravina said: "On Tuesday we will tackle this issue; the primary principle is the protection of health. Italy is currently two weeks ahead, the other [countries] probably do not yet know the exact size of things.
"We'll ask UEFA to postpone the playing of the European Championship."
Italy is the worst-hit country in Europe with 368 Coronavirus deaths recorded on Sunday.
