Sources close to Jenelle tell TMZ ... she wasn't financially prepared for such a sudden split with the network when they dropped her after David killed the family dog. We're told while she did have a cosmetics line, it wasn't that successful and she needed the cash.

We're told Jenelle -- who has now split from David -- is trying to set up a meeting with the network in NYC.

Jenelle's pitch, we're told, is simple -- she was a ratings grabber when she was on the show, and although it may be for the wrong reasons, her profile is even higher after all the drama and legal troubles with David. People who knew nothing about "Teen Mom" know her.

She also plans to tell the network there should be a measure of fairness here ... she did nothing wrong. David was the problem, and now that she's jettisoned him, all should be good.

She wants back on the show stat ... in time for the holidays. She thinks a Thanksgiving and XMAS sans David would make for good TV.