Pellè, 28, was absent from Feyenoord's squad as they took on ASWH in pre-season.
Whilst other players who were left out of the squad watched on from the stands, the lack of Pellè was prominent.
The Italian forward has been linked with a move to Southampton since the arrival of former boss Ronald Koeman at Southampton last month.
Speaking after his side's match against ASWH, new Feyenoord boss Fred Rutten confirmed that Pellè is now in the "final phase" of his move to Southampton.
Speaking to Dutch journalist Kevin Bouman after the game, Rutten confirmed that Graziano Pellè had travelled to England to complete the deal, which will see him become Ronald Koeman's second signing as Southampton boss.
Pellè's arrival will follow hot on the heels of the signing of Dušan Tadić from FC Twente earlier in the week, with the Serbian midfielder completing a move for a fee in the region of £10m.
The fee for Pellè is thought to be less than that, approximately £6m - but Feyenoord are keen to implement a number of performance-related bonuses into the deal between the two clubs.
It has been no secret that Koeman and Pellè were likely to team up together at St. Mary's, with Koeman revealing that he'd like to take Pellè to his new club before even being named Saints boss.
It is thought that Pellè has already agreed terms with the Saints and the move is subject to a medical and the final agreement of the make-up of the transfer fee between Les Reed and Martin van Geel, Sporting Directors for Southampton and Feyenoord respectively.
Southampton boss Koeman admitted in his first press conference on Friday that Pellè is close to completing the move, with the former Feyenoord boss saying that he hopes the deal will be able to complete before Southampton head to Belgium for a pre-season training camp on Sunday.
"It’s close but still not signed," Koeman revealed.
"We hope maybe this weekend to have him as the second new player of Southampton."