We typically use the prepositions "to" or "of" after "intention".
We typically use the prepositions "to" or "of" after "intention":
It's her intention to be the best student of the year.
James has no intention of retiring just yet.
While being grammatically correct, we don't normally use the negative construction "have no intention to do something". It sounds unnatural. We say "have no intention of doing something" instead.
They have no intention of telling her what really happened.
However, you can use a negative structure with the verb "be" and the preposition "to" ("It is not his/her/their intention to...")
It was not his intention to do that.
The compound preposition "with the intention of" is frequently used to express purpose in formal and semiformal contexts.
With the intention of improving her Spanish, she tries to interact as much as possible with Spanish speakers.
