Carrick left Upton Park to join Tottenham and later moved on to Manchester United in a £18.6million deal last summer.
He said: “I had some great times at West Ham growing up, and I always look out for their results. They have been through a tough time and it’s been a traumatic season for them, but I have always felt they would get out of trouble, and I still believe that.
“They had a good season last year and sometimes the second season can be difficult as many teams have found out. But I think they have enough quality and their recent run has been fantastic.”