Grainger, a four times medallist who won double sculls gold at London 2012 with Anna Watkins, shares with retired swimmer Rebecca Adlington the accolade of being Britain's most successful female Olympian.
The 40-year-old, who came out of retirement in 2014, switched her focus to the eight in May after she and double sculls partner Vicky Thornley failed to make the podium at the European championships and disbanded.
British Rowing said the women's eight was already a proven medal winning combination before Grainger and Thornley had asked to be considered for it.
"We opened up a process and gave them the opportunity. They have not been successful and we are now looking at next steps in a selection process which is on-going," the body said in a statement.
Britain's Olympic rowing squad is due to be named on Thursday, with 2012 gold medallists Helen Glover and Heather Stanning sure of their places after winning the coxless pair at the trials and European championships.
With the eight decided, a return to the double sculls -- in which Grainger and Thornley qualified at last year's world championships -- or a place as a reserve appear the only remaining chances.
"It has put my Olympic place in the balance," Grainger said in May of the decision to disband the sculls partnership.
"I’ve never been in this position before, not having a seat in a boat so close to an Olympics. But I don’t want to walk away from it now."
(Reporting by Alan Baldwin; Editing by Robin Pomeroy)
