Well, package just doesn't take variables. You could wrap the package declaration and the methods therein into a string eval. However, apart from demonstrating that it can be done I can not imagine a problem which can't be solved in an other, more reasonable way.

use strict;
use warnings;

package My;
use Data::Dump qw(dump);

my $pkg_sub = __PACKAGE__ . '::A';

my $package_declaration = "package $pkg_sub;";

eval $package_declaration . <<'EndOfPackage';
sub new {
   my $class = shift;
   bless [@_], $class;
}
# some more methods
EndOfPackage

my $new_object = $pkg_sub->new( qw( a b c) );
dump $new_object;

# prints: bless(["a", "b", "c"], "My::A")

1;
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No. Don't do this.