Staff have been locked out of the Bootle site for five weeks after protests against redundancy pay and selection criteria turned sour last month.
Unite has accused the company of targeting its members through its selection criteria, while MMP is in the process of taking disciplinary action against four employees who allegedly caused damage when the plant was occupied last month.
With no sign of movement from either side and MMP management apparently unwilling to enter into discussions with the union, Unite has gone directly to investors.
In his letter to investors, McCluskey, who has attended a protest at the plant, warned that MMP has subjected its workers to a "totally unfair disciplinary process and intimidation from hired security guards".
He said: "The company has issued redundancy notices to members of the Merseyside workforce despite a willingness on the part of the workers to meet to resolve the dispute.
"I am writing to you as an investor in MMP to raise this matter with the board and management of MMP at European level and at UK level. I also request that you press the company to enter into proper negotiations with Unite to settle this damaging and unnecessary dispute."