The Blues boss believes it will take some time for the Blackburn Rovers defender’s future to become clear this summer.
And Cowley is prepared to sit tight and see how Carter’s situation develops under new boss Jon Dahl Tomasson.
The Londoner knows, however, Pompey will likely have to fend off a number of rivals for Carter’s services - if he departs Ewood Park.
The 22-year-old has made it clear he would like to test himself in the Championship, after two successful League One loans at Burton Albion and Fratton Park.
The path to doing that with Blackburn became a little clearer earlier this month, after captain and central defender Darragh Lenihan joined Middlesbrough after becoming a free agent.
Meanwhile, Jan Paul van Hecke has returned to Brighton after a loan stay and versatile Ryan Nyambe is set to leave.
Tomasson took training with his new players for the first time yesterday, after the Dane received his work permit following his arrival as Tony Mowbray’s successor.
Cowley thinks the former Newcastle striker will now need time to assess his options before deciding what lies in wait for Carter.
He said: ‘I think we have to be open minded.
‘No one can really read the situation, Blackburn didn’t have a manager until last week.
‘He will naturally take some time to evaluate his squad, and we will see off the back of that.
‘There’s no doubt off the back of how well Hayden did for us there will be a lot of interest in him, if Blackburn aren’t to keep him in and around their group.’
Pompey will be keeping an eye on developments at Blackburn over the coming weeks, but Cowley feels he can’t get weighed down with what is taking place at other clubs.
He has his own squad reshaping to oversee in the coming weeks and months, with Marlon Pack the first summer arrival over the line on Wednesday evening.
Meanwhile, West Brom keeper Josh Griffiths is moving closer to sealing a loan move to Fratton Park as Gavin Bazunu’s successor, according to reports.
Pompey’s striking department requires some major surgery this summer, with no senior front men contracted.
Spurs front man Kion Etete is high on Cowley’s list of targets, with a contract on the table for Aiden O’Brien.
Cowley is clear his focus has to lie on the areas he has control over when it comes to his recruitment.
He added: ‘Ultimately our focus has to be on us.
‘We’ve got enough on our plate already without thinking about what is going on at other clubs and what their situation is.’