Arthur revealed that he, along with Sri Lanka captains Dimuth Karunaratne and Lasith Malinga, discussed plans to return with the board in a meeting held last week.
The fast bowlers will be the first players to return to training once cricket resumes, the former South African, Australia and Pakistan coach said.
Arthur told ESPN Cricinfo: “Last Wednesday we had a quick meeting [to talk about resuming cricket] because we are starting to get out plans in place for June 1.
“Once we get the official go-ahead from the [Sri Lanka] ministry of health I will start putting meat into that structure with the captains and my support staff.
“It is looking good with the health ministry, but it will be a smaller group.
“We’ll probably prioritise our fast bowlers because they are the ones who are going to need more time to get back into it.”
Arthur also did say that they will have to stick to the parameters being finalised by the ICC Cricket Committee (of which he is a member) before players can return to train.
The Sri Lanka mentor continued: “Once we get some assurances from the medical staff around the world that biosecure [environment] is fine and what the virus could do to you potentially if you got it.
“Once the players understand and digest they’ll all be good. And then hopefully after the first 20 days of June we could virtually have our whole squad back training.
“That’s the time for me where, if we could be in this biosecure environment, we could go in may be Hambantota or Pallekelle just for a week and try and rekindle that trust and check where we want to go with our goal setting.”