Grant was impressed with Green's mental toughness at Ipswich.
But Grant said: "Rob Green is a fantastic goalkeeper. I didn't know him before but he has a strong mentality. He knows how to do his job.
"We have made it very clear that Scott Parker will stay with us.
"We have plans for next season but also beyond that, there is a vision at the club. I want to put West Ham in a good place, playing good football. He is a big important part of that."