The Netherlands international featured for the Hammers in the victory over Bournemouth and the 58-year-old says he is considering signing him up
West Ham manager Sam Allardyce will consider whether to offer trialist Orlando Engelaar a contract over the coming days.
The 33-year-old Netherlands international is training with the club and featured as a second-half substitute in the 2-0 pre-season win over Bournemouth on Saturday.
Engelaar has been capped 14 times during a career that has seen him represent NAC Breda, Racing Genk, Twente, Schalke and PSV.
He was released by the Eredivisie runners-up at the end of last season and Allardyce will now consider whether to take him on a more permanent basis.
"A player of his experience and his quality, we'll have him with us for a few days to see if he could be a valuable member of our team," he told West Ham TV.
"We'll obviously make that decision in the near future."