That opportunity will come next week as shareholders meet to ratify a deal struck between the club and a Malaysian consortium headed by Datuk Chan Tien Ghee.
Trust Board member and financial expert, Keith Morgan, said that the purchase of the shares would fulfil a commitment made to fans that signed up as "Phil Dwyer" members.
He said: "The Trust is pleased to be able to buy shares in the club at a time where there is so much optimism about the future of Cardiff City.
"The Trust was set up to give fans a voice in how the club is run and purchasing shares gives us that representation."
The announcement comes as the Trust fast approaches the milestone of having 1,000 members since its inception in September 2008.
"Currently we have just over 980 members and we hope to reach 1,000 in the coming weeks," Mr Morgan continued.
"We will be starting a major drive in the coming months to attract new members with 2,000 our next target. The more members we have, the louder our voice will be."