The Uruguay international has been strongly linked with a move to Turin, and it is understood that personal terms have already been agreed between the two parties.
Suarez will need an Italian passport in order to represent the Serie A champions, though, as their quota for foreign players has already been filled ahead of the 2020-21 campaign.
Pirlo has suggested that the delayed process in securing Italian citizenship means that a deal for the experienced striker in this transfer window is unlikely.
"Suarez is difficult because the times to get a passport are long, it is complicated that [our new striker] can be him," Gazzetta dello Sport quotes Pirlo as saying.
Suarez has been told that he can leave Barca this summer despite scoring 21 times and registering 12 assists in 36 appearances for the club last season.