BST has sent an open ‘letter of intent’ to Oyston, who bought the club for £1 in 1987, urging him to sell “and thereby prevent any further damage being done to Blackpool FC, its reputation and its future prospects”.
Blackpool were in the Barclays Premier League five years ago but have since been relegated to the third tier.
Fans have protested loudly at the way the club has been run for the last two years and relations between them and both Owen Oyston and his son Karl, the club chairman, reached rockbottom at the end of last season.
BST said in its letter: “The action you take in responding to this bid is just as important to the future of the Football Club as was your decision to buy the Club for £1 in 1987.
“The question now facing you and your family is whether you still care enough about the well-being and reputation of Blackpool FC to sell it (ie. your complete shareholding in Segesta) to the Trust for just over £16million.
“The club is now perceived to be in such a parlous state that our members have decided it is better to offer to buy our club back by giving you as many of the assets as possible than it is to continue with the Oystons in charge.
“The actions taken by Karl over the last four years have ensured that any good that you and your family may have done for the club has been entirely negated and rendered worthless.
“You have lost the goodwill and the confidence of the supporters and indeed the people of the Fylde Coast.”
Karl Oyston was last month banned from football for six weeks and fined £40,000 by the Football Association for calling supporter Stephen Smith “a retard” and telling him to “enjoy the rest of your special needs day out” during a text-message exchange last November.
The chairman was also involved in a public fall-out with club president Valerie Belokon at the start of last season and has issued legal proceedings against several fans for defamatory comments made about him and the club.
The club prompted fury among supporters ahead of last season’s final game against Huddersfield at Bloomfield Road by removing the statue of 1953 FA Cup final hero Stan Mortensen from outside of the ground ahead of a proposed fans’ protest.
No explanation was offered by Blackpool but Lancashire Police later revealed the club took the steps themselves to remove the statue which was returned the following week.
Tensions came to a head on the final afternoon of last season against Huddersfield when Blackpool fans staged a pitch invasion early in the second half, forcing the home game to be abandoned.
The Football League elected not to replay the game but charges were brought against the club by both the League and the FA, while the incident proved to be final straw for manager Lee Clark, who quit shortly afterwards.
Neil McDonald, former assistant manager at West Ham, has since been appointed as Clark’s successor.