Advincula, 25, spent last season on loan in Portugal with Vitoria Setubal, playing 26 games before heading out to Copa America this summer.
The right back - who can also play as a right winger - was part of the Peru side which stunned the world to reach the semi-finals, and his impressive displays appear to have attracted plenty of interest.
Libero report that West Ham are keen to bring Advincula to the Premier League, but the Hammers face competition from three other clubs in what has become a four-way battle for his signature.
The report states that Benfica, Rayo Vallecano and now Sampdoria have registered an interest in signing Advincula this summer, having impressed so much at Copa America.
Hoffenheim could choose to keep him, but having loaned him out on three separate occasions, it's more likely that they will look to cash in this summer - and West Ham now face a real battle to bring him to Upton Park.
Two right backs needed?
West Ham will want to see last season's loan star Carl Jenkinson return to East London, but the departure of second choice right back Guy Demel leaves Slaven Bilic slightly short of options at right back.
Advincula's ability to play at right back and on the right hand side of midfield would make him a versatile option for West Ham to sign, offering competent cover for Jenkinson.
The Hammers will now have to pull out all the stops to sign Advincula, with a real battle emerging for his signature after his Copa America displays - though the lure of the Premier League could tip the balance in West Ham's favour.