Kean walked out on the club on Friday claiming that the situation had become "untenable."
The Rovers Trust want a stake in the club and are raising the cash in an attempt to make sure they can play a part in the decisions at the club and hopefully steer away from anymore mistakes being made.
Wayne Wild, co-chairman of Rovers Trust, told Sky Sports: "A lack of executive leadership has put the club in its worst position for 20 years.
"The need to change the manager is a perfect time for the owners to begin to build bridges with supporters.
"A new manager may offer a brief moment of optimism, but the owners really do need to address matters off the pitch, where a lack of leadership and communication has left the commercial operation of Ewood Park in an appalling mess.
"Now is an excellent time for the owners, either directly or through their appointed representatives, to enter into dialogue with Rovers Trust and begin the process whereby Rovers supporters can take a direct and positive stake in the ownership of their club.
"This is the only way the owners can truly win back the Rovers fans and the community in Blackburn.
"If they want a thriving, successful club, with the whole town behind the team, then they must accept that Rovers supporters want a say in the running of the club."