"Any player will tell you, you just want to play football," BBC Sport quotes Cole as saying. "I had a great season in France and then to come back and not for it to happen at Liverpool was hard. It would have been very difficult to turn this club down when they came in for me.
"There are a lot of old memories. You can have all the money and all the medals but on a Saturday afternoon there is nothing I like more than to be playing football."
West Ham are currently 12th in the Premier League.