Hasselbaink has joined Steve McClaren's staff at FC Twente and Southgate told the Sunday Sun: "Someone said I should have signed him last year!
"He was excellent in his time here and I'm sure he'll be good whatever he turns his hand to, because he's very enthusiastic and dedicated. Whatever he does, he'll want to do well.
"He's doing his coaching badges and he's got good opinions on the game. I enjoyed working with him. He's had that upbringing through Dutch football and played in Europe, in Portugal and England. So he's got good experience.
"I think he'll want to pass that experience on. I don't know if he wants to coach or manage but whatever he wants to do he'll do it wholeheartedly, and want to make a success of it, that's for sure."