The Blues are said to be set to bring in the Sweden international to alleviate their defensive woes.
Milosevic is out of contract after the skipper left AIK Stockholm, with his last appearance arriving in November.
Swedish outfit Sportsbladet are reporting the 33-year-old is in England undergoing a medical, ahead of a deal being confirmed for the former Nottingham Forest man.
Milosevic has nine international caps with Sweden to his name, with his last outings coming in the Nations League against Norway and Slovenia in 2022.
The 6ft 4in man boosts Pompey’s centre-back options, with John Mousinho without the services of Conor Shaughnessy, Hayden Matthews, Rob Atkinson and Ibane Bowat at present.
Pompey are able to register Milosevic, after keeping a space open in their 25-man squad registered with the EFL after the close of the transfer window last month.
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