According to the South London Press, the keeper is wanted by Pompey's League One rivals as he heads towards a Fratton Park departure.
The Blues have opted against taking up a clause in MacGillivray's contract for an additional 12 months.
MacGillivray won't be short of suitors as a free agent, having been named The News/ Sports Mail Player of the Season for 2020-21.
Since arriving from Shrewsbury on a free transfer in June 2018, the 28-year-old has made 135 appearances for the Blues in total.
Now the South London Press reports the Scot is being eyed by Charlton who'll be challenging Pompey for promotion again next campaign.
Ben Amos served No1 stopper at The Valley throughout this season but his deal comes to a conclusion at the end of June.