The possibilities that have gained some acceptance so far are these five: Jeong Jeong, Iroh, Zuko, Azula, or a new character. Here are the pros and cons raised so far to each one (with some of my own thrown in):

1) Jeong Jeong:
Pros: unarguably has mastered his element, already has a master student relationship with Aang; the creators wouldn't have created the character if they didn't intend to show him more than once (arguable).
Cons: He's old, and every member of the Gaang is in the 12-15 range (if he joined he would inevitably try to become the leader of the Gaang as the only adult); he's a one-shot character who was only in a single episode and was never seen again (arguable); Aang and the Gaang do not have time to go searching for a firebending teacher when they don't know were he is since they only have 20 episodes left after this season; eh is too powerful, his addition will make it impossible to present sufficient challenges to the Gaang.
Chance: 5%


2) Iroh:
Pros: Single most knowledgeable firebender to appear in Avatar, baring Roku who is dead, and understands his element including how to generate and deflect lightning and (presumably) blue fire; he is subservient to Zuko's wishes, meaning that if he joined the Gaang he wouldn't try to take over; his character is one of the most popular on the show, allowing him to join the Gaang would give him more screen time; he is for balance in the world, which is what the Avatar is ultimately about
Cons: He is outside the age range of the Gaang (12-15), so younger viewers would be unlikely to relate to him; there has been some foreshadowing that his character is going to die (debatable); he is too wise and powerful, his addition to the would add so much power and knowledge of the inner workings of the Fire Nation as to make it to small a challenge to defeat it
Chance: 20%

3) Zuko:
Pros: One of the most powerful firebenders shown (able to defeat Zhao, Katara, many professional and elite soldiers, and others), surpassed by only Jeong Jeong, Iroh, Roku, and Azula (and her old crone teachers); foreshadowing in many episodes, especially "The Blue Spirit"; slowly coming into opposition of the Fire Nation (from heir apparent, to exile, to dispossessed, to fugitive, to ...); in the proper age range (same age as Sokka); one of the most popular characters on the show, and with comparable screen time to Aang
Cons: Does not represent his element/has no special knowledge of firebending/can't create lightning/isn't a master bender (all basically the same reason); loyalty to the Firenation/pride will not allow him to teach Aang
Chance: 60%

4)Azula:
Pros: Master firebender, one of the best in the show, only one shown definitively able to create blue fire; in the proper age range to join the gang (younger than Sokka); is in the opening credits with Master Pakku, the male version of Toph, and what appears to be Aang or another airbending monk who are all good guy's
Cons: Single most loyal character to Ozai; doesn't care about anyone (see recruitment of Ty-Lee) or her own safety (see the conclusion to The Chase) and would therefore be difficult to convince to join the Gaang (also she is psychotic and evil); if she joined the Gaang so would Ty-Lee and Mai which would eliminate the opposing group to the Gaang, and make the Gaang very powerful, too powerful for the Fire Nation to likely be able to stop; her personality is such that she would demand that she lead the Gaang
Chance: 5% (being generous)

5) New Character:
Pros: The new character has the possibility of having all the pros listed above, except those related to popularity; The creators have done it before with Toph, so they could do it again
Cons: little time left to establish and integrate a new character; it's been done, and is therefore unlikely to occur again (Avatar's writers are not that lazy)
Chance: 5%

6) Aang doesn't learn firebending at all (anymore than he already has from Jeong Jeong):
Pros: He said he would never firebend again; little time remains for him to learn to firebend, and defeat the fire nation
Cons: The Avatar is supposed to master all four elements; it would be difficult to defeat the Firelord without mastering all four bending arts; especially if he runs out of time and has to defeat the Firelord when the comet comes (if Aang knows firebending, his skill in that is increased with all the other firebenders)
Chance: 5%

you know that firebender in the theme song? that's azula. the waterbender is pakku, and the earthbender was the original version of toph. she was originally supposed to be a dude, but... anyways, pakku taught aang waterbending(though it is now katar's job), toph taught aang earthbending, and as much as i hate to say it, azula is the only non-aang persong left in the theme song, so she might teach aang firebending. don't get me wrong, i want it to be zuko or iroh, but... man, now i'm sad. and this whole message started with me rewatching tales of ba sing se to prove to my friend that aang's hair does not look like an old man's.

they could always learn it in one place. they're not obligated to travel around unless toph finds someone chasing them

You guys have got it all wrong. The person who will teach Aang firebending is Johnny Storm. Of course, this is after Marvel Entertainment acquires Nickelodeon and the Fantastic Four join Avatar.

Either that or Zuko.

If there was something hidden in Airbending, Aang already knows it. Aang has confirmed himself as an Airbending Master.