The Icelandic international has recently been linked with a move to Leeds.
At the weekend there was a new development regarding the future of Bjarnason.
It had previously been reported that the Icelandic international was available on a free transfer at the end of the month.
However Italian source Calcio Mercato report he is still under contract with Pescara until 2017 and would cost somewhere between €2.5 and €3 million.
Palermo and Torino are now known to have bid for the player and last night another team seemingly made their move.
AlfredoPedulla.com report that Atalanta have made a bid involving €1.1 million and two players, midfielder Roberto Gagliardini and striker Matteo Ardemagni.
What does this mean for Leeds?
The growing belief seems to be that Bjarnason will be leaving Pescara this summer, but not Italy.
Leeds were first linked with a free transfer for the player but now it appears he is going to cost a considerable sum, their interest appears to have run cold.
Despite new Leeds boss Uwe Rosler working with Bjarnason when Viking boss, that sort of money is unlikely to get sanctioned for such a deal.