The 20-year-old has been in sensational form this season and has already scored over 30 goals.
And now Cole, who played nearly 300 games for Chelsea, has urged his old side to go and seal a deal.
“They need one player for me, Haaland. He’s on the wishlist,” Cole told BT Sport.
“He’s a No9. There’s so much in this squad, there’s quality in all areas, such a strong squad.
“You just need that one sparkle of magic, that No 9, that focal point and it will change this club getting back to the glory days of challenging for the title regularly.”