Two straight parallel conductors are kept horizontally one above the other. If the upper wire suspends in air without any support, then the direction of flow of current in the wires should be

The upper conductor experiences zero net force. 

$\overrightarrow{\mathrm{F}}={\overrightarrow{\mathrm{F}}}_{\mathrm{g}}+{\overrightarrow{\mathrm{F}}}_{\mathrm{m}}=\overrightarrow{0}$

${\overrightarrow{\mathrm{F}}}_{\mathrm{m}}=-{\overrightarrow{\mathrm{F}}}_{\mathrm{g}}=-\mathrm{mg}\hat{\mathrm{j}}$

Force between the conductors must be repulsive to counter the weight. 

So, currents in the conductors must be in opposite directions.