Reports in the Hampshire media claim Posh have made a move for the 28 year-old who was a runaway winner of the Pompey player-of-the-season award after playing in all 46 League One games.
MacGillivray is out of contract at Fratton Park so would not command a fee.
Posh are seeking a goalkeeper to put pressure on current first-choice Christy Pym, preferably one with the physique to combat the greater physical challenge of the Championship. MacGillivray, who has also played for Walsall and Shrewsbury, is 6ft 2ins, Pym is listed as 6ft, both on Soccerbase.com
Pompey were linked with a move for Posh full-back Dan Butler yesterday (May 16). Butler is a former Pompey player.
Posh could not be contacted for comment this morning.