Left-arm quick Amir is in line to make his Test return -- having already made his comeback in white-ball international cricket -- in the series opener against England at Lord's next month.
It was during a Lord's Test against England six years ago that Amir and two Pakistan team-mates were involved in the deliberate bowling of no-balls -- the trio having been lured into a newspaper 'sting' operation to demonstrate their willingness to take part in spot-fixing.
He has now served that ban and, unlike 2010 Pakistan captain Salman Butt and fellow paceman Mohammad Asif, Amir has now been included in the squad for a four-Test series starting at Lord's on July 14.
"It's kind of ironic that his first Test match will be here back at Lord's," Cook told reporters at the ground on Wednesday ahead of the third Test between England and Sri Lanka.
"But I have no problems in playing against him at all."
However, the left-handed opener added: "My only thing is that if you get caught match-fixing, you should be banned for life.
"The punishment should be that hard, because we've got to protect the integrity.
"That's not saying Amir shouldn't come back, because the rules were probably different then.
"From my point of view, the punishment should be harsh to try to deter people from doing it. But that's from now on, that's if I had any say in it.
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