Cole thinks Chelsea should only sign a forward to compete and support Abraham, not take his position.
“Well, you certainly don't need to replace him," Cole said on BT Sport. “I think he has made himself irreplaceable as a member of the group at Chelsea because he's a young lad who epitomises what the club is about.
“He knows the club and that's without the stuff that he's doing on the pitch.
“On the pitch he's been fantastic, he's scored goals, he's lead the line, he's been a revelation.
“But what Chelsea, and any of the top clubs will do, is they will always look what's around: 'Can we improve? Can we improve?'.
“So I think unless they're going to bring in someone who is going to compete with him, not to go above him or below him as a youngster - someone to compete with him.
“I believe he can [be Chelsea's long-term striker]. The mentality, the mindset and when you've got a young player with them two attributes - forget the speed, the strength, technical ability - if you've got those two attributes, you can work with that and he's just got better and better.
“We've seen it with our own eyes how he's got better over the last three, four years. He's been a revelation."