Former Manchester United trainee Ajose is on the transfer list at Posh and is expected to leave the Sky Bet League One club during the current transfer window having found first-team opportunities hard to come by since moving to London Road in the summer of 2011.
Since signing for Peterborough Ajose has had loan spells at Scunthorpe, Chesterfield, Crawley and Bury.
The 21-year-old spent some time with St Johnstone last week and remains in the thoughts of Saints boss Tommy Wright despite returning to England.
"Nicky Ajose is back away down south now to his club. We are still thinking about him," said Wright.
Peterborough have bid for Saints striker Stevie May but have yet to meet the Perth club's valuation of the Scotland Under-21 international.
Amid rumours of a possible cash-plus-player deal, Wright insists Ajose's trial and Posh's interest in May are merely coincidence.
He said: "I can state categorically it had nothing to do with Stevie May and Peterborough."