Russia's Channel One state television reported that Pavel Dmitrichenko's girlfriend, also a Bolshoi dancer, was known to have been at odds with director Sergei Filin over the parts she was being given.
Other media said Dmitrichenko himself had missed out on several top roles at the theatre.
The 29-year-old from from Moscow has danced in the Bolshoi Theatre troupe since 2002 and was to dance in "Sleeping Beauty" this month.
He could now face jail and possibly the end of his dance career.
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Mr Osborne said he is "not the person to provide the unity my party needs".