There is the possibility of Liquid Breathing, however it is unlikely that the liquid would be haemoglobin and still be breathable, as haemoglobin is quite viscous (this is why it is contained within red blood cells).
On the other hand, in the unlikely event that a planet was completely covered by an ocean of some largely colourless oxygen saturated liquid such as a flurocarbon at ~37°C, then, yes, humans could in theory breathe this liquid. It is probable that if such a planet existed, it would have been manufactured by some powerful civilisation.
However, free-breathing fluorocarbons is exhausting due to the mass of fluid involved and the amount of oxygen that could be saturated in it. Were humans to spend any length of time in such an environment, it is likely that they would need some sort of mechanical breathing assistance to prevent exhaustion.
Finally, fluorocarbons are up to twice as dense as water. This means that a human would float on the surface of a fluorocarbon sea to a greater degree than in highly saline water (such as the dead sea). However, with the mechanical assistance required for prolonged breathing and movement, neutral buoyancy could be achieved.
Finally, if this world had any significant amount of water, since flurocarbons do not mix to any great extent with water, any of the world's free water that could not dissolve in the fluorocarbon sea would likely form a layer on top of the fluorocarbon layer, over which would be any gaseous atmosphere.
The main question in this world would be how the fluorocarbon sea maintained its oxygenation.