The phrase 'curious to learn' is correct and usable in written English. You can use it when you want to express a desire to explore and discover something new. For example, "I am curious to learn more about the practice of astrophotography.".
She told me that she was curious to learn what country music was like.
I'm actually curious to learn what President Obama plans to do if he's re-elected.
(Shades from Defoe to Liebling were curious to learn of these new developments).
I'd be curious to learn if this was one or two simultaneous tests.
Diners curious to learn the true taste of the individual fish might try this offering.
At its best "Art:21" makes uninitiated viewers curious to learn more about this realm.
I'd be curious to learn what trespassers are laying waste to your own backyard garden.
When I feel like I can't trust my brain 100%, Ludwig really comes in handy. It makes me translate and proofread faster and my output more reliable.
Claudia Letizia
Head Translator and Proofreader @ organictranslations.eu