Abraham is enjoying a fantastic season in west London following a season-long loan spell at Aston Villa last term.
The England international has scored 11 goals in 14 Premier League appearances in 2019/20, proving considerably more successful than recent holders of the Blues’ No.9 shirt, including Radamel Falcao, Alvaro Morata and Gonzalo Higuain.
And Cole, who played 31 games for Chelsea at the start of his career, believes Abraham will continue to shine.
“Tammy has the self-confidence to succeed,” Cole told 888sport.
“There was a curse on the No. 9 shirt and that’s the one he wanted so that shows me that he has the confidence to believe he can come in and do a job for the team. He’s doing that at the moment.
“Tammy right now doesn’t compare to [Jimmy Floyd] Hasselbaink and [Didier] Drogba because they were class for their era.
“Hasselbaink had his days as a No.9 doing his thing; a renowned goalscorer. And obviously Drogba did so well at every level right up to Champions League.
“He is very different to the No.9s that Chelsea usually have. I don’t see him as a big, powerful No. 9. He can move to the left and right and could easily play as a No.10. He’s that good.
“But he’s being used as an out-and-out striker and he can do that job as well. He loves to score goals. He loves to get into the penalty area. He’s not one of those guys who will shoot from outside the box: he’s a goal-poacher.”