The 23 year old joined the Hammers from Deportivo Maldonado on a season-long loan deal last summer, having previously spent the first six months of 2016 on loan at Sao Paulo.
Jose Jacobson, Sao Paulo's director of football, is convinced Calleri is keen to return to Brazil but believes a transfer is unlikely with his club not willing to sanction another short-term deal.
"I think we lack a number nine," he told Globo Esporte. "Otherwise, I think we're well prepared for this first semester.
"Calleri is interested, but there is the problem with the investor group, who paid a lot for him and want him to stay in European football, even if he doesn't stay in West Ham.
"Sao Paulo can't invest anything, it's out of our reality. A six-month loan does not interest us. I can't bring Calleri for a short time again."