Defoe, a former Irons player, worked with Moyes at Sunderland.
He told the Mirror: “I love West Ham and I love the fans. Even when they give me a bit of stick I know, deep down, that they appreciate me and I have so many great memories of the club.
“I remember walking into the training ground at Chadwell Heath as a 16-year-old, hoping I would be good enough to play for West Ham like the greats who had worn the claret and blue before.
“To break into the first team at 17 under Harry Redknapp was a special feeling, and when I'm watching Match of the Day or looking out for other results, West Ham and Tottenham are the ones I'm after.
“I'm from the East End too, a lot of my family are West Ham fans and that's where it started for me. Of course it hurts to see them going through a rough time.
“There is still a long way to go and they have a good manager who is experienced and knows his way around the Premier League.
“I liked playing for David Moyes. He didn't put any extra pressure on me or try to complicate the game. It was almost as simple as, 'You're a goal-scorer – go out there and score goals.'
“Because I'd done it over the years, there were times when he would give me the freedom to go where I wanted, to express myself and find pockets of space where the chances might come.
“On the training pitch, he's very vocal and hands-on, and training is always very sharp with the accent on quality.
“He needs time – it's not easy fighting fires and the last couple of jobs he's had have been difficult. But with the players he's got at West Ham, and the quality in that changing room, I think they should be alright."