Cole has been strongly linked with French giants Paris Saint Germain but Hasselbaink believes the Blues should give the England left-back what he wants.
The former Chelsea striker told The Sun: "With Cole, I don't understand why they're not offering him a two or three-year deal.
"Yes, he's in his 30s, but he's still very fit. On top of that, he is still the best left-back in the country - maybe even the world.
"It's not going to be easy to replace him or even find someone capable of doing it. He plays the majority of games and is almost never injured, so why not give him a longer contract?"