A group of Hibernian shareholders plan to vote against the proposed £6m investment by Billy Foley at the club's annual general meeting on Tuesday.
Should Foley's investment be voted through as expected, HSL's shareholding would take a significant drop.
The American billionaire, 79, will not attend the AGM at 18:00 GMT on Tuesday.
On the HSL website they say "we have received little context or explanation around any of the proposals and have, in the main, relied on media reports to stay engaged with the progress".
The Scottish FA have given their approval to the investment by Foley and his Black Knights consortium, who also hold a controlling interest in English club Bournemouth along with others in France and New Zealand.