The Brazil international is expected to leave Barcelona, as things stand, but is prepared to stay at the Camp Nou - even if it means taking a pay cut - if the length of the deal is longer than two years.
This is according to Spanish publication AS - and brought to our attention by the Mirror - who understand Barcelona are a little reluctant to offer Alves a new contract of such length.
Barcelona have submitted offer to Alves
Barcelona have submitted an offer to Alves, which has been confirmed by his agent Dinarah Santana, but it seems the deal on the table is likely to have been deemed unsatisfactory.
"On Monday, I had a meeting with [director] Javier Bordad. On Wednesday I have had the second meeting," Santana told AS. "I have already received an offer [for a new contract], although I can't say if I am happy or not [with it].
"There will be more meetings. They told me they will call me to arrange the next one."
Man United move still possible
Failure to offer Alves the length of contract he craves could see the South American full-back complete a summer move to Manchester United, who have submitted a formal offer to the player, according to recent reports.
Paris Saint-Germain are also keen on the 31-year-old, who ranks as one of the best full-backs of the current generation.
Barcelona would be foolish to let Alves leave
Barcelona should be doing everything in their power to keep Alves at the Camp Nou given they are not suitably prepared for the possibility of losing him on a free transfer this summer.
Alves is still the best right-back at Barcelona, by some considerable distance, with Martin Montoya and Douglas paling in comparison.
Because of their existing transfer ban, Barcelona are unable to sign a replacement for Alves until January 2016, meaning they run the risk of enduring a difficult first-half of the 2015-16 campaign without a first-class right-back.
Barcelona would, of course, still win most of their matches with Montoya or even Douglas at right-back - but the big test will come in the Champions League group stages and in league matches against the likes of Real Madrid, Atletico Madrid and Valencia.
Since Alves still has plenty to offer and is even prepared to take a pay cut, it would seem almost perverse if Barcelona opt against retaining the services of one of their most consistent performers.
Will Dani Alves be a Barcelona or Manchester United player next season? Have your say in the comments below!