The 18-year-old is currently embroiled in a bitter contractual dispute with the Spanish giants, having turned down their offers of a new deal with less than a year remaining on his current terms.
Moriba has been frozen out of the first-team picture at Barcelona as a result, and Mundo Deportivo claims that he has now told the club that he is only interested in a move to Leipzig.
However, the German outfit are understood to have made an offer of just €6m (£5.1m) for the highly-rated teenager - a long way below Barcelona's €20m (£17.1m) asking price.
The report claims that Tottenham were willing to meet Barcelona's demands and were close to completing a £17m deal, but that option is now off the table due to Moriba's desire to join Leipzig.
The Catalan outfit are refusing to budge on their asking price, though, and are willing to leave Moriba out of the first team for the entirety of the 2021-22 season before losing him on a free transfer next summer if Leipzig do not return with a significantly improved bid.
Moriba, who has reportedly already agreed personal terms with Leipzig, joined Barcelona as a seven-year-old in 2010 and made 18 appearances for the senior team last season.