The Trust owns 21.1% of Swansea City but under the proposal, Steve Kaplan, Jason Levein and Jenkins would gradually buy its shares.
The details will be included in a proposal the Trust hope to put before members at a meeting on 1 July.
The Trust recommends the proposal is accepted.
Trust chairman Phil Sumbler said the proposal would "strengthen their financial position" while at the same time keeping a stake in the club.
Under the proposal, Kaplan, Levein and Jenkins would purchase an initial 5% of the total shares in Swansea City from the Trust's holdings which would raise about £5m.
On top of the initial 5%, there would be another 0.5% every year for the next five years, subject to the club staying in the Premier League.
There is also an option for a possible sale of a further 3% in the next two and a half years. That would total 10.5%.
If the deal is ratified the Trust, following legal advice, says it would be obliged not to pursue any legal action regarding an alleged breach of a shareholders' agreement by the former directors who had sold their shares as part of the Americans' takeover in 2016.
No definitive date has been set for any ballot to vote on the proposals but the Trust believe it could happen imminently and hope it could coincide with the meeting on Saturday in which board members are elected.
Swansea City Supporters Trust could sell up to half its current shareholding to the club's American owners and chairman Huw Jenkins.