After a tricky second round Tiger Woods tried to regain lost ground on Saturday, but his four-under round of 66 was not enough to make much of a difference.
He rose one place up the board to sit tied in 11th on 12 under overall.
It was a better day for Open Championship winner Francesco Molinari, whose 64 pulled him 13 places up the board to tie for seventh.
The Italian Ryder Cup squad member fared better than wildcard team mates Paul Casey and Tyrrell Hatton, whose rounds of 69 saw them both plunge 12 places into joint 50th.
Ian Poulter, who will also be heading to Spain, carded a 67 to climb four spots into 44th and go five under overall.
A win in Philadelphia should be enough for Rose to take the crown of world number one from Dustin Johnson.
The American, along with world number two Brooks Koepka, were tied in 33rd after round three on eight under overall.
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