A report from Football Insider earlier this month suggested that Pompey, Ipswich Town and Charlton Athletic were all weighing up a move for the Luton Town forward.
Discussions between Hylton and Luton over a new deal at Kenilworth Road are currently ongoing.
If an agreement cannot be reached, the 33-year-old will become a free-agent when his existing contract reaches a crescendo at the end of June.
As per TWTD, Ipswich have not reportedly expressed an interest in Hylton.
Portsmouth are also understood not to be in the running for the former Oxford United man.
Pompey head coach Danny Cowley will need to bolster his options up-front this summer following the departure of George Hirst.
Hirst returned to Leicester City last month after his loan deal at Fratton Park expired.
Hirst is set to be handed the chance to prove his worth at Leicester when the Premier League side reports back for pre-season training.
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When you consider that Hylton only managed to score four goals in 22 appearances for Luton last season, there is no guarantee that he will be able to excel in the third-tier next season if he joins a club in this division.
Keeping this in mind, it is hardly a surprise that Portsmouth are not pursuing a move for the forward.
In order to have the best chance of pushing forward as a team next season, Pompey will need to nail their recruitment this summer in this particular position.
Having recently reached fresh agreements with Sean Raggett and Michael Jacobs over the futures at Fratton Park, Portsmouth will now be focusing on signing an individual who possesses the ability to spearhead a push for promotion by finding the back of the net on a regular basis in the third-tier.