Anfield officials say interest in the forward has increased over the weekend and a move abroad is the most likely outcome after Premiership duo Aston Villa and Everton dropped out of the chase.
Baros has again been withdrawn from the squad travelling to Bulgaria tomorrow as his future looks to be resolved.
Funds from the Baros transfer have already been set aside to pay for a new centre-half, although the Reds' chase for Deportivo's Jorge Andrade is likely to end in frustration. The Spanish side insist their defender is not for sale.