The former Everton defender moved to the Danes on-loan from Atalanta last month.
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And Godfrey has made an instant impact - both on and off the pitch - with Brondby. Cooper said: "He has already proved to be a strong leadership figure in the squad. It's clear to see he's a big winner.
"It's clear to see he has quickly built a relationship with his teammates. I hope we can benefit greatly from him this spring."
On Godfrey signing permanently, Cooper added: "He has to train well, deliver on the field. So far, I like what I see from him.
"Now it's about the next match. Then we have to take the dialogue when the season is over."