Alves has enjoyed seven successful years at Barcelona, winning four Spanish titles and the UEFA Champions League twice.
But the 31 year-old has been unable to agree a new deal with the Catalan club and will leave the Nou Camp at the end of the season.
Dinorah Santana, the player's agent and ex-wife, said at a press conference on Thursday that her client had rejected the offer of a three-year contract extension, which was dependent on the player taking part in 60 per cent of matches for the club.
"The negotiations are over," she said.
"If they say this is the final offer, then they (negotiations) are over.
"It doesn't make sense. It's very hard that we get to April and Barcelona haven't thought about renewing Dani's contract.
"Dani is sad."
The news that Alves is to leave is likely to spark a scramble for the defender's signature.
The ex-Sevilla full-back has been linked with Manchester United and Manchester City, as well as Paris Saint-Germain.
Santana said Alves has two offers on the table at the moment, but has not yet been approached by big-spending PSG.
"He has had conversations with future candidates," Santana said.
"PSG have not made an offer, but we have two offers of three years."
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