Reports have suggested the Blues are going to attempt a summer swoop for the talented 20-year-old.
The forward spent the first half of the 2021-22 campaign on loan with Cheltenham where he impressed in Michael Duff’s side - scoring four times in 13 league starts.
Joseph was recalled in January and has since appeared 10 times for Russell Martin’s outfit in the Championship.
Following speculation of a summer move by the Blues we spoke to Gloucestershire Live’s Cheltenhan reporter, Jon Palmer, who gave us an insight into the Swans forward from his time at Whaddon Road.
Here’s what he had to say.
‘Kyle made a really positive impression at Cheltenham, and at one stage of the season he kept player of the season Alfie May out of the team!
‘He scored four goals in 13 starts which is pretty respectable. Given his height at 6ft he’s very good in the air. He's got a good, athletic spring on him, winning long balls forward and surprising everyone with his defensive qualities, his clearances and heading out from set pieces.
‘One of his best performances actually came at right wing-back. He played there against Gillingham, because he’d played a bit there before he joined.
‘He’s one of those players that can do everything because he’s quick and quite good in the air. He’s not just just a poacher, he can do more than that. He’s not a target man either, but has attributes to do everything.
‘Cheltenham wanted to keep him, but he was recalled by Swansea because they wanted to give him a go and he’d shown he is fully capable of succeeding in League One.
‘Pompey will want to be challenging higher up the league next term, and I’d back Joseph to be capable of playing a part in a very good League One team – because he did that well at Cheltenham.
‘I don’t want to say he’d be another John Marquis, I think he’s better, but when he came to Cheltenahm at a similar age to Joseph, there are certain things about his game that reminded me of Marquis.
‘Marquis is a worker and sometimes his finishing lets him down, but I think Joseph has got that and a little bit of finesse to his game as well.
‘He’s further ahead at the age he is than when Marquis came on loan from Millwall in 2014 - and he still went on to do very well in League One.
‘He’s on course to have a very good career and if Pompey can get him, then I think they’re going to get a player that will be a major asset.’