Dinorah Santana said Barca had offered the 31-year-old a deal that could stretch from one year to three should he play in over 60 percent of his side’s games each season.
However, Alves has been heavily linked with a move to Paris Saint-Germain and Manchester United among a host of other top European clubs and Santana said he had better offers on the table from other clubs.
“He would accept three years, but the condition that a player plays 60 percent of the games every year for me is not a three-year deal, but a one year,” said Santana.
“Dani has a concrete offer on the table for a three-year deal plus the option for an extra year with a better wage than he has here and a signing on fee.
“Barca at the moment have told me that they will not match those figures and we understand that.”
The Brazilian has made over 300 appearances and won 16 trophies at the Camp Nou since joining from Sevilla in 2008.
His absence would cause Barca major problems for next season as the club are banned for registering new players until January 2016 due to a FIFA sanction for irregularities in the signing of minors.