The England international left-back has been delighted with the impact the Dutch tactician has had on the squad since he arrived on a temporary basis following the sacking of Luiz Felipe Scolari in February. And, having guided the Blues to the Champions League semi-finals, the FA Cup final and kept them in the race for the Premier League title, Cole is hoping he could be persuaded to extend his stay with the Londoners.
"He has got everything. The lads just love him," said Cole. "He can be funny and likes a laugh but he can be serious and when he is serious you know he is serious and he does a great job.
"All managers have a scary side. But he wasn't so much scary - he just made us realise we needed to do something.
"If he needs to put an arm around you then he will. He is not one of those who will leave you on your own to deal with things. He will come over and look after you and tell you things you want to hear.
"He has been a breath of fresh air with the players. He has given us all a belief, he has come in and just made everything click so easily. He has been so good for us.
"It will be sad when he goes. All the players would love him to stay. I definitely would. I don't know what he is thinking or what he can or can't do. We hope he stays, that is all we can do."
However Hiddink remains adamant that he will be leaving Stamford Bridge this summer and return to his role as boss of the Russian national team on a full-time basis.