Since Maz is force sensitive, was she ever approached by the Jedi with the intention to send her to the Jedi temple? If so, did her parents not let her go or something?
There is no evidence that she was.
While there is certainly room for such an encounter to be added into canon, as of right now, there is no such event.
The Star Wars Databank basically encapsulates all we know about Maz's background.
Maz Kanata is more than a thousand years old, a diminutive being with vast experience at surviving in the underworld.
Maz Kanata | Databank
Maz was born over a millennium before the events of The Force Awakens. Probably right around, or just before, the time of the Jedi-Sith war that featured Darth Bane (called the New Sith Wars in Legends). Aside from Darth Bane establishing the Rule of Two, we really don't know anything about this time period (anymore). The Jedi could have had a different method of discovering force-sensitives, or Maz simply could have been over looked like Anakin was.
This would not be an unlikely scenario as Maz was raised, and then lived in, the criminal underworld of the galaxy. She was born on Takodana (the one we see her on in TFA), which is in the Mid Rim. The Mid Rim is unofficially considered the edge of Republic space, due to the level of enforcement they (don't) have over any of the sectors further out.
So in short, there is no evidence to suggest Maz was, or could have been, approached by the Jedi. Out-of-universe, there is certainly room for this to be added to canon, but it has not happened yet.
During the rise of Darth Sidious, Maz didn't share her force sensitivity with anyone. We can assume then that she was fairly open about it before, so it is easy to imagine that the Jedi contacted her, if not for training but at least for assistance. However, we know that the padawan selection process is not perfect (see Anakin) so it's also reasonable to think that the Jedi just didn't find her, especially given that at the time of her padawan years, the Jedi Order was still shaken up by the Brotherhood of Darkness