At the end of the January transfer window, the 29-year-old Croatia international was poised to join the Clarets, in something of a drawn-out saga.
Clarets chairman Alan Pace travelled to Croatia to try and wrap up a deal, but Dinamo then put out a statement on their social media channels, saying: "In recent days, great interest from the public and fans has been causedby the possible transfer of Mislav Orsic to the English club Burnley.
""Continuing on this topic, GNK Dinamo informs the public that the decision has been made that Mislav Orsic remains a Dinamo player and we look forward to participating with his teammates in the rest of the season and contributing to achieving the goal with his games, in winning the new title of Croatian champion."
A fee had been discussed, believed to be in the region of what Dinamo wanted for the player - around £7m.
And the Croatia international was also thought to be happy with the terms on offer at Turf Moor, and unconcerned by the prospect of relegation.
However, the sticking point appeared to have been Dinamo wanting the fee paid in full immediately, rather than in instalments, with subsequent stories in Zagreb of Dinamo rejecting an offer of €10m - around £8.3m - and wanting him to play instead in a key top of the table clash with Rijeka.
There was opposition to the move from fans, with banners hung outside Orsic's home saying ‘Orsa ostani’ - ‘Stay Orsa (his nickname), quoting the track 'Noć je prekrasna’ by Daleka Obala, which basically means 'don’t go away from us; the darkness is all around'.
And Dinamo Zagreb fans, the 'Bad Blue Boys' took to the streets of Zagreb with banners and flares, again begging Orsic to stay.
So Orsic finished as Dinamo top-scorer for the fourth-successive season, with 20 goals in all competitions, as the side won the title, netting vital goals against Hajduk, Osijek and Rijeka.
But it has been suggested in Zagreb by germanijak.hr that “everything was agreed for Oršić to move to Burnley at the end of the season, provided that the club stays in the (Premier) league. That didn't happen, though. Burnley dropped out and thus the transfer of Mislav Oršić to the most lucrative league in the world failed.”
Orsic could still move to the Premier League, as, according to Sportske novosti, four clubs are interested in the player, potentially including Leeds, who survived on the final day at the expense pf Burnley.