The fast bowlers, who both played in England's 75-run defeat by Pakistan in the first Test at Lord's, were released ahead of the second Test, which starts at Old Trafford on Friday.
Now fit-again fast bowler James Anderson (shoulder) and all-rounder Ben Stokes (knee), who both didn't play at Lord's, are set to make their Test return in Manchester.
England seek Saqlain’s help to counter Yasir threat
England's decision means they could give a home debut to leg-spinner Adil Rashid, all of whose three Test appearances to date were away to Pakistan in the United Arab Emirates last year.
"We're going to name a 12 -- Steven Finn and Bally are missing out," Cook told reporters at Old Trafford on Thursday.
"That means, obviously, Ben Stokes and Jimmy Anderson are back in - and Adil's going to be in the 12, just depending on what happens to that wicket by tomorrow (Friday)."
Won’t panic if England lose second Test against Pakistan: Jonny Bairstow
Revised England squad:
Alastair Cook (c), Alex Hales, Joe Root, James Vince, Gary Ballance, Jonny Bairstow (wkt), Ben Stokes, Moeen Ali, Chris Woakes, Adil Rashid, Stuart Broad, James Anderson
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