Ali took just two wickets during a 75-run defeat by Pakistan in the first of a four-Test series at Lord’s last week.
By contrast leg-spinner Shah, Pakistan’s specialist slow bowler, had man-of-the match figures of 10 for 141.
Yet for much of his career 29-year-old off-spinner Ali has been regarded as a top-order batsman.
The Worcestershire all-rounder found himself thrust into the role of England’s frontline spinner following the retirement of Graeme Swann during England’s 5-0 Ashes thrashing in Australia in 2013/14.
Ali’s 27 Tests have yielded 68 wickets at an expensive average of over 41 apiece.
By contrast, the 30-year-old Shah has taken 86 wickets in just 13 Tests at an average of 23.
England added leg-spinner Adil Rashid to a 14-man squad for this match and kept him in a 12 announced Thursday.
But England captain Cook, speaking to reporters at Old Trafford on Thursday, made it clear that Rashid would play in addition to Ali, but not instead of him.
“Moeen is our first-choice spinner for this match,” Cook said. “If we go with the four seamers and one spinner Moeen will be that spinner.”
It is 16 years since Chris Schofield became the last England leg-spinner selected for a home Test.
All of Rashid’s three Test appearances to date came away to Pakistan in the United Arab Emirates last year where he took just eight wickets at an expensive average of 69.50.
Cook said the Yorkshireman was making encouraging progress, having starred in England’s recent one-day series win at home to Sri Lanka.
“He really impressed in that one-day series. He is improving all the time and he bowled really nicely in the nets today.”
England had few answers to Shah at Lord’s but, despite the short turnaround, Cook was confident they could play him better at Old Trafford.
“One thing he does very well is he doesn’t bowl many bad balls, which is the skill of a great spinner,” said Cook.
“How many wickets has he taken in his first 13 matches? He is up there with the greats.
“When he bowls bad balls you have to cash in and he is obviously the linchpin of their bowling attack.
“They rely on him and if we can play him better it will put pressure on their other bowlers.”
Cook added, “The great spinners I’ve faced I remember facing (Sri Lanka’s Muttiah) Muralitharan for the first time and the first 30-40 balls you are thinking you are never going to score a run against him.
“But the more time you get against him, you get more in.”
No England batsman made a hundred at Lord’s and opener Cook, whose first-innings 81 was his side’s best score, admitted: “Lack of runs cost us.”
Both Ali and James Vince, yet to make a fifty in his four-Test career, were guilty of reckless shots in the second innings.
England coach Trevor Bayliss has encouraged the side to play positively but Cook was adamant the Australian was not urging players to lose their heads.
“Trevor’s big thing is being positive in defence and attack,” said Cook.
“Maybe in some of those shots we didn’t get that balance right.
“These guys likes James Vince and Alex Hales have only played a handful of Test matches and will take time to learn and get better.
“Vince has a lot of talent and has a lot of time to play his shots. I am encouraged, but like all of us they are desperate for a big score.”