Sterling's impressive form this season earned him a call-up to the England senior squad aged just 17 but discussions over a new contract with the Merseyside club have continued to stall.
Goal.com revealed last week that Manchester United had enquired about the winger's availability ahead of the expiry of his current deal at the end of next season.
But, after the 18-year-old starred again at Upton Park, Cole has insisted his fellow attacker should stay put at Anfield.
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"It was a great pass from Raheem for my goal," Cole told the club's official website. "That's what he's capable of, he is a real livewire and is always a threat.
"He never stops running and working hard for the team and never looks tired, and for an 18-year-old kid that's unbelievable. He is going to be a top player and he is at the right club to do that."
Cole also reserved praise for 20-year-old Jonjo Shelvey, who led the line for Liverpool in the absence of the suspended Luis Suarez.
"Jonjo is such a clever player and he was a credit to the team today," Cole enthused. "He worked his socks off, he held the line and he was always a threat."