One close to the bidding said such agreements appeared to put Fortress far ahead of Apollo in the deal planning.
Apollo is not thought to have sounded out the government on its potential interest either.
Concerns have been voiced in Westminster about US private equity companies buying up UK plcs, with Morrisons becoming something of a lightning rod for populist opposition.
Fortress, which is bidding with the backing of Canadian pension fund CPPIB and a division of Koch Industries, will need to win over 75% of Morrisons’ shareholders if it is to win.