Alessandrini decided to join the MLS side on transfer deadline day after falling down the pecking order at the Ligue 1 club.
He had scored 31 goals in France before his switch and that form caught the eye of Hull boss Marco Silva.
A number of clubs within Europe were interested in his services, but any move to the KCOM Stadium was ruled out when he agreed to join the Galaxy.
When asked, Alessandrini refused to deny there was interest from Hull, although he did not name any potential suitors.
He told L'Equipe, "If I was to stay in France, I would have preferred to stay at Marseille.
"The other options were interesting, but moving to the USA really was a tempting gamble, and a really different one at that."