The Finland international failed to impress after joining the Parkhead club from German side Schalke 04 in 2013.
He was farmed out to the Copenhagen side and managed better than he did in Scotland, scoring nine goals as he helped Brondby finish third in the Danish top flight. The 25-year-old has now been rewarded with a three-year contract by boss Thomas Frank after finishing the season as his top scorer.
Despite registering seven goals in his first season in Glasgow, Pukki never came close to justifying the £3 million fee former Celtic manager Neil Lennon paid for him.
Meanwhile, Celtic will not be making bids for Scotland forwards Steven Fletcher and Ikechi Anya – because they cannot afford their huge wages.
Reports have suggested the Parkhead club are keen on Sunderland’s Fletcher and Watford winger Anya. But Collins Speaking at Edinburgh Castle following the release of the 2015/16 Ladbrokes Scottish Premiership fixtures, Deila’s number two said: “I don’t think I can say they’re players that we’re trying to sign.
“They’re two good football players who I admire but they’re both Premiership players so the reality is they’ll be on Premiership wages, so probably out of our wage bracket.”
Collins also confirmed the path was clear for Rangers to re-sign Danny Wilson from Hearts after revealing Deila “won’t be pursuing” the 23-year-old defender who began his career at Ibrox before moving to Liverpool.