The Italian has been linked with moves to the Toffees and Chelsea after Ronald Koeman switched to Goodison Park and Antonio Conte moved to Stamford Bridge.
Italy's Graziano Pelle celebrates after scoring
It may be that at some point this summer though, the striker, who scored 14 times last season, is faced with a crisis of where his loyalties lie.
He will naturally be grateful to Southampton for the opportunity to play in the Premier League, and the international recognition that has brought. The 30-year-old's impressive form for Italy at the European Championships has seen his stock rise and it is good to hear that he is looking forward to working with Claude Puel.
However, Ronald Koeman of course knows what the striker is capable of, having worked with him at both AZ Alkmaar and Feyenoord before bringing him to the Premier League as soon as he took over at St Mary's.
Southampton manager Ronald Koeman acknowledges fans at the end of the match
With the future of Everton striker Romelu Lukaku likely to be uncertain until the closing of the transfer window, it wouldn't be a surprise if the Dutchman urged the Toffees to go big with a transfer approach for the Italian if the Lukaku leaves.
Similarly, he is highly thought of by new Chelsea boss Antonio Conte, who called him up early in his tenure as Italy manager and had him lead the line for the tournament in France. Under Conte, Pelle scored seven goals in 17 matches for his country.
If either club come at Southampton with a big offer, Puel may be willing to accept the boost to his transfer kitty for a player that will turn 31 this summer.
Italy's Graziano Pelle in action with Sweden's Erik Johansson