This is a definition of 'intrigue' in the Oxford Dictionary.
[transitive] to make somebody very interested and want to know more about something
Considering that adjective 'interested' is usually followed by preposition 'in', I think it is better to rewrite the definition as follows.
to make somebody very interested in and want to know more about something
Am I wrong?
"Interested" may be followed by a prepositional phrase "in..." but it's not mandatory. The thing that interests you may be implied by context.
There's a job advertised as a gardener. What do you think?
Yes, I'm interested, and I might apply for it, if the pay is enough.
There is no need to treat this as a phrasal verb "interested in". There is no need to insert "in" in the quoted definition.
