The Daily Mail says amid rumours of serious dressing-room unrest, the Stamford Bridge hierarchy are understood to be hugely disappointed with Grant's failure to rise to the occasion at Wembley.
In particular, they were shocked to see him on the periphery when coach Steve Clarke delivered a team talk between the end of normal time and the beginning of extra-time.
The Israeli seemed to have the full support of his employers when they handed him a four-year contract in December and he also had their public backing when the club announced their financial results last week.
Chairman Bruce Buck said: "We judge a manager on results and, to date, his results have been very, very good." Before Sunday, his record was impressive. In 34 games since succeeding Jose Mourinho he had won 24 and drawn eight.