Dolan, 47, is undergoing a course of chemotherapy following an operation to remove a tumour from his bladder.
The Irishman has brought hundreds of players through the academy over more than a decade with the club.
Graduates Steve Sidwell, Shane Long and Jem Karacan are among those to have used #21forDolan on Twitter.
The number 21 follows a suggestion by fans website The Tilehurst End to stand for a minute's applause in the 21st minute of their opening home Championship fixture against Leeds United on Sunday.
It also recognises Dolan's long-time post as manager of the under-21 side.
In a statement issued by the club, Dolan expressed his thanks for "the superb support and medical care" he has been given since his operation.
Dolan's playing career, which included appearances for West Ham, Birmingham and Exeter City was cut short in 1993 when he was diagnosed with testicular cancer.
He was also appointed Reading caretaker manager for one match following the dismissal of Brian McDermott in 2013.
Reading supporters and players past and present have shown their support for academy manager Eamonn Dolan on social media.