The 30-year-old was released by the Upton Park outfit at the end of last season, but rejoined on a short-term contract in October due to a shortage of strikers, including Andy Carroll's continued absence with a heel problem.
Cole's deal is set to end next month, but three goals in his last six league appearances - including strikes against Manchester United and Arsenal in the last two fixtures - have done his chances of earning a prolonged stay no harm.
But West Ham have lost four of their last five top-flight fixtures, with Thursday's 3-1 setback against Arsenal leaving the club in the bottom three.
And Cole is desperate for Sam Allardyce's side to start picking up points.
Speaking to the club's official website, he said: "All I care about is winning.
"I don't look at those sort of (goal) stats, I just want to win games. Next time we go out on that field if I'm starting, I just want to win that game."
Despite the setback against Arsene Wenger's men, Cole feels West Ham can take confidence from a spirited performance into Saturday's encounter with fellow strugglers West Brom.
"If we play like that against West Brom then I think we've got a chance of coming away with a better result than that," he continued.
"We did the best we could with our resources but we just have to take the positives out of the game."
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