The 21-year-old scored 12 goals for the Red Devils last season, including strikes against Manchester City and Arsenal, and netted the winner for England in their 3-2 win over Sweden at Euro 2012.
Cole, who signed for Manchester United for £7 million in 1995, is backing the young striker to establish himself as a world-class English forward.
|TOP SEASON FOR DANNY?|
|20/1||Danny Welbeck is 20/1 to be top scorer in the 2012-13 Premier League season with bet365|
"[Chicharito's] injury last season gave Danny the chance to shine and he took that opportunity. He's done very well for himself. He got himself into the England squad and, again, he made the most of that chance. First and foremost, he's not let himself down at any stage.
"So this is going to be a big season for him. He has to try and cement his spot as a first-choice Manchester United striker. He's more than good enough to do that, but he has to keep doing it. You have to do it season in, season out before people are convinced by you."
Cole, who scored 121 times for Sir Alex Ferguson's side in six seasons, believes that now is the time for Welbeck to choose what direction he wants to take, and what style he feels will suit him best.
"All I can say is that Danny has the attributes required to score plenty of goals," Cole added. "But he needs to decide what sort of striker he wants to be. Does he want to be a great goal-scorer or a scorer of great goals?
"Look at the goal he scored for England against Sweden, and some of his goals for United last season. He's got that predator's instinct.
"He can be that sort of player, but he needs to decide is whether or not he wants to be a 20-goal-a-season man or somebody who chips in with 10 or 12 screamers into the top corner."