And the Daily Mail have reported how the Chilean head coach is now interested in bringing Shawcross to London Stadium ahead of the new season.
Relegated Stoke are on the hunt for a new strike partnership next season and they have reportedly shortlisted Wolves star Benik Afobe and Watford's Andre Grey as potential new recruits for a combined £30m.
But the Potters would need to recoup some funds from selling players this summer, the first of which looks set to be Xherdan Shaqiri who could be available for as little as £12m.
Gary Rowett's side could also be tempted to offload Shawcross this summer to free up space on their wage bill as the 30-year-old is pocketing £55,000-a-week on his current deal.
There has also been some uncertainty surrounding the future of Joe Allen but Stoke seem eager to tie the Wales midfielder down to a new contract at the bet365 Stadium this summer.
West Ham are also eyeing some attacking signings this summer and the club are rumoured to be "really close" to completing the £38m signing of Lazio's star winger, Felipe Anderson.