Driver Iain Gillham, 53, was paralysed from the waist down when the 200-tonne tower crane toppled over on July 6, 2009, smashing into the apartment block at the Chandlers Wharf development just off the Strand.
The Liverpool Echo reported that local consulting engineer Bingham Davis and contractor Bowmer & Kirkland appeared at Liverpool Crown Court accused of breaching health and safety regulations.
They will reappear for a plea and case management hearing next week.