Waqar was forced to step down in April after a row with the Pakistan Cricket Board over the leakage of his confidential report on the team performances in the Asia Cup and World T20 which also led to his ouster. The PCB has now appointed Arthur on a two-year contract.
Waqar, 44, admitted he misses working with Pakistan, as he wanted to help the national team compete with top teams of the world.
"Any player, who has served the country for 10 years or more wants to see the team do well and not stay behind the rest of the world," the former Test captain told the 'Express Tribune' newspaper.
"There was some unfinished business and I will hopefully comeback to Pakistan cricket one day to complete it."
Waqar also stepped down himself during his first tenure as Pakistan coach in 2010-2011.
Waqar also welcomed his successor's wish to interact with him before the tour of England begins, stating he is just a call away if Arthur needs his help.
"The tour of England isn't going to be easy for sure, but self-belief of achieving something in testing conditions can do wonders. It would have been a challenging task for me and it would be the same for Arthur.
"Arthur has coached around the world so the required experience is there, but again it all comes down to how players respond to a coach's or captain's call," he added.
Reflecting on the team's chances in the Test series against England, he said Pakistan can trouble England especially with their bowling line-up.
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