package XYZ;

my( %instances );
sub new {
  my $class = shift;
  my $self = bless \$class, $class;
  $instances{ $self }{ hash1 } = { something => 'this' };
  $instances{ $self }{ hash2 } = { something_else => 'that' };
  return $self;
}

sub method {
  my $self = shift;
  my( $hash1Ref, $hash2Ref ) = @instances{ $self }{ hash1, hash2 };
  print $hashRef1->{ something }, $hashRef2->{ something_else };
}