The midfield duo have both been sidelined with knee injuries, with Messi requiring an MRI scan after being forced off in the 2-1 win over Lyon last week.
L'Equipe reports both players should be in the squad to face City on Tuesday, with Verratti - and potentially Messi - set to return to training next week.
PSG revealed Messi has started running once more in a statement on Friday, with the forward set to undergo a further check on Sunday.
"As you've seen in the medical update which comes out before the press conference, we are going to assess him," he said.
"We hope he improves and on Sunday we will be able to give a positive update. We hope everything goes well and he will be available again.
"We hope he can play (against Man City). We have to be cautious to see how he evolves in the next few days."
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