Duncan has acted as a mentor to Cole for his entire career.
The striker said: "He is my worst critic - I don't care what my mum, Sam Allardyce or any papers say about me.
"He is the most supportive because he is the one I am scared of.
"My uncle should be the one to go in and see the chairman at the end of the season.
"He was like a dad to me growing up and helped me through everything. He took me to training and when I was on loan to Wolves and Villa he lived up there with me.
"He has been through thick and thin with me. He has been the backbone to my career so far and without him I'd be lost.
"I'd love to stay at West Ham. I have been here seven years. Once we're safe, hopefully something will be sorted out - I don't want to go anywhere else. "It can't be West Ham or nothing, though, because I am still only 29."