Rachel Uchitel has just told a very close friend ... now that Tiger Woods is single, she wants him back and would "give up everything" to get him.
The friend -- someone we know spoke to Rachel yesterday -- tells TMZ Rachel said ... "I feel horrible for him. He loved her. But he was in love with me. I hope he remembers that was real, and reaches out to me."
Rachel added, "I'd give up everything to be with him again."