The Guardian reports that the Brazilian offered part of his liver to teammate Eric Abidal when the Frenchman needed a transplant in 2012.
The selfless offer was gracefully declined by Abidal as it would have seriously impinged on his friend's career.
In honour of Alves' altruism, here follows a selection of players past and present who have shown generosity, character and a public spiritedness beyond the call of duty...
Didier Drogba isn't the only footballer to redirect some of his earnings to African charitable causes, but the Galatasaray striker's generosity is overwhelming.
In addition to setting up and maintaining the Didier Drogba Foundation—which aims to improve children's health and education in Africa—the powerful striker once donated the full £3 million fee he received from a Pepsi endorsement to build a hospital in his native Ivory Coast.
Chelsea midfielder Michael Essien siphons a significant proportion of his salary to his own foundation, which helps the underprivileged in the Awutu region of Ghana where he was raised.
Essien has held star-studded charity games to raise awareness for his foundation's cause and it is thought he gives up to a third of his salary away to help the less fortunate.
In April 2007, Sunderland won a crucial Championship game at Cardiff. As players and staff boarded an Easyjet plane in Bristol destined for Newcastle, many Black Cats supporters started singing the bizarre anthem "Niall Quinn's Disco Pants" in honour of their chairman and former striker.
Unfortunately, the raucous chanting led to several fans being thrown off the plane and the subsequent cancellation of the flight.
When around 100 fans were left stranded 320 miles from home, Quinn booked 14 taxis, putting the £8,000 charge on his credit card.
Over the summer, Leeds United fans who had made the trip all the way to Slovenia to see their team in action were treated by manager Brian McDermott.
When chants of "Oh Brian, it's your round!" filled the Slovenian ground, the former Reading boss duly obliged and handed over €50, which was all the cash he had, so the travelling supporters could buy a pint or two.
At Slovenian prices, €50 goes quite a long way...
Craig Bellamy may strike you as a golf club-wielding, nightclub-brawling maniac, but the Welshman also has a selfless side.
Despite hailing from Cardiff, the Bluebirds striker has his own charity foundation in Sierra Leone. He visits the football academy most summers, he personally interviews the staff who work there and he has donated more than £1 million of his own money since 2007.
When he first travelled there with a bag of balls, his then-club Liverpool refused to insure him as the region had only just emerged from civil war.
Everton fan Gordon McKee will be watching every Toffees home match this season, thanks to the club's Make Their Day initiative.
In April, Leighton Baines personally delivered the season ticket, a bouquet of flowers and a signed shirt to the man whose wife had recently lost a five-year battle with a brain tumour.
The act wasn't Baines' own initiative, but the moving footage of the goodwill gesture shows his compassionate side.
In March, Edgar Davids' Barnet lost a match at Accrington Stanley, after which 36 Bees fans were left stranded on the long ride home when their bus broke down.
When the team bus zoomed past the unlucky supporters on the M6 motorway, Davids insisted that the players be dropped off at the next service station so the fans could be picked up and brought to that service station where they could wait for alternative transport in the warm and mingle with their heroes.
A man who headbutts his way out of a World Cup Final may appear to be quite self-regarding, but Zinedine Zidane boasts an extensive range of charitable contributions.
In addition to featuring in and helping to organise charity matches for the likes of Unicef, Soccer Aid, the Manchester United foundation and children's AIDS charities, Zizou has been a UN goodwill ambassador since 2001.
The World Cup winner helped set up the UN's Match against Poverty, which has been running annually since 2003.