The unnamed reserve team regular has little experience of first-team football but Posh are keen to find striking reinforcements to replace Aaron McLean, who joined Hull on New Year's day.
And director of football Barry Fry has confirmed he is hoping to conclude more signings soon.
"The plan is the new boy will be here on Thursday in time for training," Fry told the Evening Telegraph.
"We are also in talks with other players and clubs, but one problem is that clubs know we have a bit of money to spend and so ask for more than we want to pay.
"Mind you I'm exactly the same when teams come on asking about our players."