Reports also state that Arthur has sought two more years to deliver "remarkable results".
This comes after PCB's Cricket Committee reviewed the side's performance over the last three years.
This included the 2019 World Cup where Pakistan could not qualify for the semis.
Arthur wants Shadab and Azam as Pakistan captains
The report suggests that Arthur has told the board that Shadab Khan should be the candidate to replace Sarfaraz as captain in white-ball cricket.
Shadab is one of Pakistan's most prominent rising cricketers. He is a valuable asset in their ranks.
Meanwhile, Babar Azam is Arthur's choice to take over the reins of the Test side.
Promising Azam is Pakistan's leading batsman across formats.
'Arthur had negative comments about Sarfaraz's captaincy'
"Arthur did have some negative things to say about Sarfaraz's captaincy skills to the members. I need two more years with the Pakistan team and then I can deliver remarkable results," a source said to PTI.
Ehsan Mani to decide on new team management
PCB's Managing Director Wasim Khan is believed to be keen on having another session with the members on Wednesday.
Post that he will be forwarding recommendations to board Chairman Ehsan Mani regarding the appointment of the new team management.
Meanwhile, the contracts of Arthur and other support staff members will expire on August 15.
A look at Arthur's tenure as Pakistan could move on
Arthur is most likely to be let go as Pakistan coach.
He took over the mantle in mid-2016.
Under his tenure, Pakistan won the ICC Champions Trophy in 2017.
The team also grabbed the number one spot in the ICC's T20 Rankings.
Pakistan's performance in Test cricket dipped drastically and in ODIs too they kept struggling.
A new direction is what Pakistan might seek.
What next for Pakistan cricket?
Notably, Arthur's presentation to the Committee on team performance and selections, is said to have left the members unimpressed.
It remains to be seen how the board goes about in terms of captaincy and coach.
Pakistan have identified key players and youngsters will hold the key.
However, the path to gaining instant success won't be easy.