The 21-year-old has scored nine goals in all competitions this season, including strikes against Manchester City and Arsenal in recent weeks.
Cole believes that Welbeck's form has proved invaluable considering the injury problems that Javier Hernandez has suffered so far this year.
"I think Danny's brilliant, and it's fantastic for his confidence that he's starting so many big games," Cole told the club's official website.
"Javier Hernandez has been injured and has been finding it tough to repeat what he did in his first season. Sometimes your second season is your toughest, I went through that myself.
"Danny has come in and grabbed his chance with both hands and he's playing very well. He's playing with confidence and getting goals too."
Cole scored 121 goals during a six-year spell at United.