Tim Tebow -- Hardcore QB Training in L.A. ... I'm Not Giving Up!!!

Tim Tebow has NOT YET abandoned his dream of becoming a starting NFL quarterback -- and spent his Tuesday running through grueling QB drills at a private field in L.A. ... TMZ Sports has learned.

Despite reports that Tim has hired an agent specializing in on-air talent, Tim appeared pretty focused on PLAYING the game during a training session at USC.

Sources at the field tell us ... Tim spent 4 hours on the field -- spending a good chunk of the time working on throwing mechanics.

We know ... Tim has been a regular at the school for the past couple of weeks -- training almost every day with a personal trainer who seems to be focused on Tim's throwing motion.

It's interesting ... considering most "experts" believe Tim's pro career died when he was cut by the New England Patriots before the season began. Clearly, Tim's not giving up hope.

TMZ Sports reached out to Tim's camp for comment -- so far, no word back.