Lee is scoring goals for fun at U21 level this season.
Fletcher told talkSPORT: "It would be great [to see Elliot Lee get a game]. West Ham have got a fantastic tradition of bringing kids through the youth set up with Tony Carr down there. There is an endless list of internationals he has brought through.
"It would be nice to see a young person come through at West Ham again and just give him a chance."
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