Cole is putting his faith in the quartet of new boy Javier Hernandez, Michael Owen, Federico Macheda and Danny Welbeck (unless he departs on loan) to provide ample back-up to Wayne Rooney and Dimitar Berbatov.
"Hernandez looked sharp at the World Cup for Mexico. He has a good eye for goal," Cole told the Manchester Evening News.
"The two young lads Macheda and Welbeck didn't get much time last year and so they will be hungry this season.
"And as for Michael Owen, if he stays fit then he can come in with a fair few goals. He scored nine last season yet only started 11 matches. Even used sparingly if Michael is 100 per cent then you would expect him to score around 10-15 in a campaign. If by some chance he plays most matches then he is still a 20-goals a season player.
"I take my hat off to Chelsea for the number of goals they scored last season. It was fantastic but it is not often anyone outscores Manchester United and I think we can score enough this season to win back the title."