Nick Young claims the woman who accused him of rape back in 2011 has demanded $3 MILLION in damages to make things right … but the NBA star is refusing to budge … TMZ Sports has learned.

As we previously reported, Swaggy P is being sued by a woman who claims Nick slipped her a date rape drug at a Hollywood bar in 2011, took her to his house and vaginally and anally raped her.

Cops investigated the alleged incident and DISMISSED her claim because they felt her story didn’t add up. The woman filed a lawsuit against Young in 2013 … and the two sides are still battling it out.

Now, according to new docs obtained by TMZ Sports … the accuser has a number in mind — $3 million … claiming she suffered emotional distress and loss of earnings.

But Young isn’t buying it — and has refused to settle … instead, fighting the case tooth and nail to prove once and for all he’s no rapist.

A hearing is scheduled for later this month.