The Blues CEO also cast doubt over a second loan arrangement for the defender by claiming the Championship side currently have ‘big plans’ for the 22-year-old next season.
Yet he stressed, if that changed – with Rovers currently in the process of searching for a new manager – then Pompey would be very interested in a reunion with the player.
Carter enjoyed an impressive loan spell at Fratton Park over the second half of the 2021-22 season.
He made 22 appearances and scored once as he settled in automatically to his new PO4 surroundings.
His form has since prompted the Blues to register an interest in bringing the £500,000-rated former Manchester City youth-team player back to the south coast.
Yet, so too is the prospect of returning to Ewood Park to fight for a first-team place for the Championship outfit under their yet-to-be-confirmed new manager.
That certainly acts as a stumbling block to any Pompey move for a player who can comfortably operate at right-back or in the centre of defence – as does Rovers’ apparent stance on Carter.
According to Cullen, he is likely to be ‘a big part of their team going forward next year’, with his Fratton Park loan designed to facilitate that progression.
Speaking to BBC Radio Solent, the Blues CEO said: ‘Hayden is a player that everyone would love to have back at Fratton Park, not just myself and Danny, but the supporters as well.
‘We’re in a situation with Blackburn where we were very grateful to them for entrusting the next stage of Hayden’s development with us in the second half of last season.
‘I know they have big plans for him at Ewood Park and at the minute see him as a big part of their team going forward next year.
‘They don’t even have a manager at the minute, so that has to play out.
‘When we signed him, it was very much on the basis that this was a precursor to him being a big part of Blackburn’s plans going forward.
‘We’ll continue to monitor that one and if there’s any chance of us having Hayden back then we’d love to have him again here next season.
‘If we could do a permanent then fantastic, but I think that’s relatively unlikely given Blackburn’s plans for him.’