Koeman wants Pelle, 31, to follow him to Goodison Park after scoring 26 Premier League goals in two seasons under the Dutchman at Saints.
But the Italy ace, who netted twice during his country’s run to the Euro 2016 quarter-finals, has been offered the chance to more than double his wages by joining
Shandong in a deal that will net Saints £13m.
Pelle is in the final year of his Saints contract and has not been offered a new deal at St Mary’s.
The former Feyenoord front-man was also wanted by Juventus and Lazio.