Mistakes will always be made in French, and now you can learn from them.
Wrong: Je suis intéressé dans
Right: Je suis intéressé par, Je m'intéresse à
Explanation: "Je suis intéressé dans" is the literal translation of "I'm interested in." However, as is often the case, the literal translation simply isn't good French. The correct way to say "I'm interested in" is je suis intéressé par or je m'intéresse à:
Je suis intéressé par votre offre.
I'm interested in your offer.
Je m'intéresse aux sports.
I'm interested in sports.
Être intéressé par and s'intéresser à are pretty much synonymous, though s'intéresser à is a bit stronger, implying that some effort goes into understanding or participating in the subject or activity.
Note that the phrase être intéressé dans does exist in French, but means "to be part of, to be involved, implicated in":
Savez-vous qui est intéressé dans ce scandale ?
Do you know who is involved in this scandal?
Related lessons:
Pronominal verbs
Verbs with prepositions

