The firm is thought to be the favourite to replace Carillion as the main contractor on the £335 million scheme, with work having ground to a halt following the company's collapse into administration in January.
Unite made its call after claiming Laing O'Rourke is 'well known' for being anti-union with an 'especially poor' history on Liverpool hospital projects
The union said during Laing O'Rourke's time as main contractor on the Alder Hey hospital project, the company refused to allow unions access to the workforce and barred the appointment of union safety representatives.
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In addition, Unite said the development had a 'very poor' safety record, with five accidents on site during the space of a fortnight in 2014. Injuries to workers included broken limbs and one employee suffering a crushed pelvis. Other problems included the refusal to allow known trade union members to work on the site and the extensive use of bogus self-employed labour.
Unite added the problems were so severe they were raised as part of the Scottish Affairs select committee investigation into construction blacklisting.
Unite assistant general secretary, Gail Cartmail, said workers on the Royal Liverpool Hospital project "have been in the frontline of Carillion's collapse".
"It is now imperative that a new contractor ensures that workers' rights are protected and the highest safety levels adhered to," she said.
"It would be a disgrace if this flagship project was completed by a company boosting its profits by exploiting workers, ignoring workplace rights and cutting corners on safety. We will be working with local representatives to ensure our concerns are listened to, and further delays to the project are avoided."
(LM/MH)
