Previously published experimental work by other authors has shown that certain motile marine bacteria are able to track free swimming algae by executing a zigzag path and steering toward the algae at each turn. Here, we propose that the apparent steering behaviour could be a hydrodynamic effect, whereby an algal cell's vorticity and strain-rate fields rotate a pursuing bacterial cell in the appropriate direction. Using simplified models for the bacterial and algal cells, we numerically compute the trajectory of a bacterial cell and demonstrate the plausibility of this hypothesis.