The News understands the Blues are interested in a loan move for the 22-year-old this month, as they look to bolster their backline.
And past reports on the 22-year-old will make pleasant reading for the Fratton faithful.
The versatile defender has been called upon by Tony Mowbray 10 times this season, with the Lancashire club pushing for promotion to the Premier League.
Carter also spent last season on loan with Burton in League One – making 25 appearances while scoring four goals.
That’s led to a positive assessment of his time with the Brewers by manager Jimmy Floyd Hasselbaink.
He told The Burton Mail: ‘He came in with no League experience whatsoever and he made that place his own.
‘Since he came in there has never been a doubt in our minds to take him out.
‘Only in one or two matches has he had a problem with his opponent. The majority of the time he has really bossed the strikers around.
‘He has a bright future.
‘Do I think he can play in the Championship week in, week out? Yes, eventually.
‘There is still stuff he can improve but that is just experience, having the time to develop. He has been brilliant, brilliant, brilliant for us.’
After his impressive spell at the Pirelli Stadium, Carter was handed a bumper new contract at Ewood Park in the summer.
And at the time, Mowbray explained how the 22-year-old was fully deserving of his fresh deal.
The Blackburn boss told Lancashire Live: ‘I think he warrants a new contract.
‘He's come back from his loan with Burton and he's grown another inch, his chest is sticking out a little more and he's more muscular to cope with the physicality of this division.
‘It was a big ask of him to go and play right-back the other night but we're pleased with Hayden, he was superb.
‘We're pleased he's signed a new deal and hopefully he has a big future to the football club.’
Following his breakout season for Blackburn, Carter’s list of admirers appears to be growing.
However, the starlet has kept his feet firmly on the ground
Here’s what he said on his own future and where he flourishes on the pitch.
Speaking to Lancashire Live he said: ‘I'm not too bothered where I play, if I get an opportunity I'll take it.
If it's at right-back then I'll adapt my game to what's needed.
‘I don't have a preference, although I think I'm better as a centre-half (as) I've played there all through my youth career.
‘However old you are, however experienced you are, there's always something you can learn from the game.
‘In terms of positioning and using your body and stuff like that, it comes with experience.’
A message from the Editor, Mark Waldron