The youngster is one of many subjects that the club will hash out with their new head coach.
The Hammers are focused on finalizing the integration of Julen Lopetegui and his staff to replace the departed David Moyes.
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Southampton, where Downes spent a year on loan, want to bring him back permanently.
As the Saints are now in the Premier League, they will be a serious option for Downes.
However, West Ham will have the final say on his future, with Downes stating recently: "I can't say too much, we'll see what happens."