Simon Cowell -- I Want Britney Spears on 'X Factor' ... BADLY

Simon Cowell has finally admitted ... he's GUNNING HARD to get Britney Spears as a judge on the next season of "X Factor."

Cowell just called in to "TMZ Live" ... and told us, "I would love to have her on the show ... I think she would be a fascinating person to sit next to."

Simon said he couldn't reveal too much about the negotiations ... but did seem optimistic and hinted that he would have an answer from Britney's camp within the week.