The transfer has been dragging on, with the Clarets discussing a fee for the 29-year-old, which was believed to be in the region of what Dinamo wanted for the player - around £7m.
And the Croatia international is also thought to be happy with the terms on offer at Turf Moor, and also unconcerned by the prospect of relegation.
However, the sticking point appears to have been Dinamo wanting the fee paid in full immediately, rather than in instalments, and there have been subsequent stories in Zagreb of Dinamo rejecting an offer of €10m - around £8.3m - and wanting him to play on Sunday in their top of the table clash with Rijeka.
There were also banners outside what is believed to be 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 on Thursday night, journalist Ižak Ante Sučić of germanijak.hr (@IASucic) tweeted a photograph of Dinamo Zagreb fans, the 'Bad Blue Boys' in the streets of Zagreb with banners and flares, again begging Orsic to stay.
There were unconfirmed reports that he said his goodbyes to his team mates and staff on Thursday morning, but with Dinamo seemingly dragging their feet, Pace has made the trip to Zagreb to try and smooth things over, with Monday's 11 p.m. transfer deadline looming.