Aston Villa are looking to sign a new goalkeeper this summer.
Gollini, who currently plays for Verona, is a transfer target for Roberto Di Matteo - but the deal could be a difficult one to force through.
Although Villa have made a £3 million offer for the 21-year-old, he is reportedly unsure over whether a move to the Championship would benefit him.
Gollini made 27 appearances in Serie A last season, and apparently feels that staying in his homeland will be better for his development.
Villa, therefore, could be forced to look elsewhere as they look to bring in a new goalkeeper this summer.
Brad Guzan and Mark Bunn both failed to convince with their performances for the Midlands side last campaign, leaving Di Matteo wanting to sign a new number one.
If Gollini does reject the chance to move to Villa, the Claret and Blues are expected to make a move for Costel Pantilimon.
Pantilimon is currently playing for Watford, and he is expected to be available for transfer this summer.