The 32-year-old is reportedly keen to return to Europe after his spell in China and would be linking up with former team-mate Jose Fonte if he made the move to the London Stadium.
However, compromises would have to be made on the Italian's salary, which is understood to be around £13.5m a season but his team Shandong Luneng are allegedly willing to cut their losses.
West Ham need to sign a striker this January after Andy Carroll suffered another injury in their Premier League match against West Brom on 2nd January which will see him sidelined for at least three months.
Pelle would be a good addition to the squad, if Moyes can get him relatively cheap, as his previous league experience is a major advantage.
The Italian made 81 appearances in all competitions for Southampton during his two-year spell in England, scoring 30 goals, before moving to China for £12m in July 2016.