Ajose, 20, played in Wednesday's friendly loss to the Premier League side Tottenham after spending time training with the Borough squad.
Now the former Iron loanee - he made eight appearances in an ultimately disappointing two-month loan spell at Glanford Park last season - looks poised to join the League One side on a permanent basis.
"Nicky has come in for us to have a look at him from Peterborough. He's still under contract at Peterborough." said Smith.
"There may be something we can do there in terms of a deal but that'll be going on behind the scenes with the chairman."
Ajose is transfer-listed at Peterborough, having dialled to fulfil his potential at London Road.
Posh signed him from Manchester United for an undisclosed fee last summer, but he managed just two appearances in the first-team before loan spells at the Iron and Chesterfield.
Alan Knill, the Scunthorpe boss who had worked with Ajose on loan at Bury, had tried to sign him last summer but interest from several Championship clubs meant it was impossible to do a deal.