According to Spanish newspaper Marca, and brought to our attention by the Daily Star, the Brazil international had planned to leave the Catalan giants on a free transfer next summer - when his contract expires - following nine years at the club.
But Barcelona boss Luis Enrique plans to offload him before the start of the 2014/15 campaign - and Liverpool could be his next destination.
Rodgers not convinced by Johnson
It's reported that Liverpool boss Brendan Rodgers is not convinced by the club's current first-choice right-back Glen Johnson, the 29-year-old England international who is great going forwards but has been criticised in the past for his defensive efforts.
However, Rodgers' pursuit of Alves - another attack-minded full-back - appears to make little sense if the Northern Irishman plans to keep things tight at the back next season.
The South American has arguably been the best right wing-back in world football over the past five years but, at the age of 31, will soon begin to decline physically.
Liverpool set to sign Manquillo
Furthermore, Liverpool are set to complete the signing of Spain Under-20 international Javi Manquillo, who will undergo a medical at Melwood later today.
The 20-year-old Atletico Madrid starlet is regarded as one for the future by Rodgers, but his first-team opportunities at Anfield would be limited by the purchase of Alves.
Rodgers will also be mindful of the fact he has Jon Flanagan at his disposal. The 21-year-old, who made his senior England debut earlier this summer, flourished last season - playing 25 matches in all competitions for the Merseyside outfit.
Watch: Dani Alves in action
Paris Saint-Germain keen
A lucrative move to Paris Saint-Germain - where compatriots Thiago Silva, Lucas Moura, Maxwell, Marquinhos and David Luiz all ply their trade - might be more appealing to Alves than a scrap for a fourth-place finish with a team who recently sold their best player.
Alves will be keen to add to his personal silverware collection before he retires - and would stand a fantastic chance of winning a Ligue 1 title next season by joining the Parisians.
Barcelona want Cuadrado
Barcelona, meanwhile, are keen for Alves to leave the Camp Nou in order to bring in Fiorentina's Colombia international Juan Cuadrado, who has also been linked with a move to Manchester United this summer.
The 26-year-old has played most of his career in an advanced right-wing position but possesses the required attributes to play at right wing-back thanks to his tremendous work-ethic and searing pace.