The 29-year-old goalkeeper will be leaving Burnley this summer after his contract expires at the end of June.
Several clubs across the English Football League are interested in getting their hands on the experienced custodian but Portsmouth are leading the race.
John Mousinho is in favour of bringing in a new goalkeeper and the club are in advanced talks with Norris.
But it has been claimed that contrary to claims, Norris’ move to Fratton Park is not a done deal yet.
The move has yet to be finalised and Pompey have not yet scooped Norris up.
Portsmouth are though very much likely to sign the shot-stopper unless something dramatic happens during the talks.
Mousinho is looking to build a squad that can challenge for promotion in the upcoming campaign after Portsmouth finished eighth in the table last season.
Norris is seen as the kind of experienced goalkeeper Portsmouth need to be amongst the top teams in League One in the 2023/24 campaign.