"He says he cannot forget me."
Translation:Er sagt, er kann mich nicht vergessen.
I agree. They are in their rightful second position within their respective clause, while other verbs or verb elements such as seperable suffixes or participles – in this case the infinitive vergessen, that is dependent on the conjugated modal verb können – are pushed to the end.
And here's an additional note that is unrelated to the question: In formal German it's better to use Konjunktiv for indirect speech: Er sagt, er könne mich nicht vergessen.