John Mousinho’s side are going through a summer overhaul to make the team competitive in League One.
And the Portsmouth boss has identified the goalkeeper position as their priority this summer.
Portsmouth want to sign Luton Town goalkeeper Macey, who spent the second half of the season at Fratton Park, on a permanent deal.
Macey joined the Hatters last summer from Scottish outfit Hibernian and has another year left with the newly promoted Premier League side.
It has been suggested that the deal regarding Macey is far from being sorted, despite Pompey’s keen interest in the player.
And it has been claimed that the Fratton Park outfit have shortlisted Norris as a backup plan if they fail to agree a deal with Luton Town.
Norris joined Peterborough on loan from Burnley in January and helped them reach the playoff semi-final by keeping ten clean sheets in 22 games.
Burnley have released the 29-year-old goalkeeper and the player is currently without a club.
