The Jubilo Iwata forward received an invitation in early December to train with the Championship outfit, and has spent the last three days under the watchful eye of Hammers boss Sam Allardyce and his coaching staff.
According to Iwata club president Hiroyuki Yoshino, Maeda will be returning to the J-League side as soon as possible.
"We understand they were unable to agree terms," he told Reuters.
Maeda, who scored 14 goals in 28 league appearances last season, will be disappointed that he may not get another opportunity to play abroad.
"At my age, this is likely my last chance to play overseas and I want to do everything possible to make it happen," the 30 year-old was quoted as saying earlier in the week.