Adrian Peterson -- Alleged Baby Mama Demands $2 Million ... Gets Stiff Arm

A massage therapist who claims she was knocked up by Adrian Peterson has asked for $1.9 MILLION to care for the kid for 18 years ... but the NFL star has fired back with a big, fat "NO DEAL."

TMZ Sports has learned ... Peterson was contacted by the woman's attorney in early August -- claiming the woman is convinced Adrian is the baby daddy and therefore needs to open his checkbook.

In fact, the woman sketched out an outline breaking down how much she'll need over 18 years ... down to the last dollar.

1. Monthly support -- $6,000 for 216 months ($1,296,000)

2. Pre and postnatal costs -- $30,000

3. Health insurance costs -- $1,000 per month for 216 months ($216k)

4. Private school -- average of $30k for 13 years ($325k)

5. Uninsured health care costs including mental health costs for the child -- $3k per year

6. Attorney's fees -- $60,000

So, how did the demand fly with Peterson's team? It didn't.

We've learned Peterson's attorney fired back a response rejecting the settlement proposal -- but said IF the child turns out to be AP's, "he will gladly agree to reasonable support."

Peterson already has a legion of children ... and his wife is currently pregnant with baby #8.