The 26-year-old has been sidelined for a fortnight after picking up a hamstring strain in the 2-1 victory against Aston Villa earlier this month.
- West Ham home
- Premier League fixtures
He missed England's friendly defeat to Brazil in Qatar on Saturday, but is pleased with the way his recuperation is going.
He said: "The Everton game was a bit too soon, but now I can just focus on Hull and try to get a result there.
"I'm trying to play well and stay up there with the top scorers in the Premier League.
"All I can do is keep tucking them away and hopefully I can progress and get to ten before Christmas, because that is my target."
Former Chelsea striker Cole has netted six league goals so far this season for the relegation-threatened Hammers.
Source: DSG
