Chelsea have scored considerably less goals this season in the Premier League than rivals Manchester City, Manchester United and Liverpool.
Alvaro Morata, who joined the club from Real Madrid in the summer, is the club’s leading goalscorer but he has missed games due to injury.
In his absence, Conte has been reluctant to pick Michy Batshuayi as his main striker and has often instead plumped with Eden Hazard in an unfamiliar position.
Cottee says that is the reason Chelsea have not been making their domination count in matches, and says a striker must be top of the shopping list in January.
“Yeah without doubt (scoring goals is their main problem),” the former West Ham man said.
“But it doesn’t help if you don’t play a centre-forward does it. Morata’s been brilliant, if he doesn’t play Batshuayi’s sitting on the bench.
“Antonio Conte obviously doesn’t fancy him, Batshuayi, if he doesn’t fancy him then just move him on in January, get someone in.
“I know it’s difficult because if you’re trying to sign a player you’re going to say ‘come to Chelsea, and you’re going to sit on the bench behind Morata’.
“I understand all that, but there must be someone out there who he can have a little bit of faith in.
“They’ve got incredible midfield players, all those chances and to not score a goal, it just lets Chelsea down. The end product is missing.
“West Ham beat them the other week and it was the same thing.
“If they want to push up the league and challenge for the Premier League every year, you’ve got to have at least two top-quality strikers, otherwise you’re not going to win it.”
Chelsea managed to find their scoring boots in the second half of their clash with Brighton today, with Morata and Marcos Alonso scoring in a 2-0 win.