The Lilywhites are said to have initiated discussions with the Brazil international, as they attempt to add an experienced title winner to their ranks.
Yahoo! Sport claims that manager Mauricio Pochettino is keen to find the right blend next season after again falling just short in their pursuit of silverware this time around, with former Barcelona ace Alves among those being targeted.
Alves won six Liga titles, three Champions Leagues and five Copas del Rey during his time in Spain, while also remaining on track for a treble during his first year in Italy with Juventus.
The Brazilian still has another season to run on his current deal in Turin, but has openly admitted in the past that he would like to one day play in England.