The News understands the Blues have made enquires about handing the Denmead lad a dream move to his boyhood club.
Butcher is on Danny Cowley's radar as he plots the latest League One promotion push at Fratton Park.
Despite being a Pompey fan – citing Matt Taylor as his hero growing up – the former Cowplain School pupil instead came through the ranks at AFC Bournemouth.
Butcher struggled to make a first-team impact at the Cherries, though, and featured only twice in cup competitions.
He had loan spells with Gosport Borough, Woking, Yeovil and Scottish Premiership side St Johnstone before leaving Bournemouth last summer to join Accrington on a free transfer.
Despite having little senior experience, Butcher proved to be one of the best performers in a Stanley side that punched well above their weight to finish 11th in League One.
In total, he made 49 appearances, scoring two goals and creating five. However, he didn't play against Pompey in either of the two fixtures towards the end of the season due to a hamstring injury.
Butcher has a year remaining on his Accrington deal so he would command a fee.
What's more, Stanley boss John Coleman has recently admitted he's under no pressure to sell and wants to keep a bulk of his side together in a bid to push for the play-offs in the 2021-22 campaign.
Still, the 24-year-old’s performances have caught the eye of the Blues as Cowley seeks reinforcements in the middle of the park.
The head coach has admitted bolstering the spine of his team as a priority during the early part of the transfer window.
Pompey are short of centre-midfielders, with not one senior option currently under contract.
Ben Close and Tom Naylor were offered fresh terms to remain on the south coast.
However, both rejected new agreements, with Close opting to pen a three-year deal at Doncaster Rovers and Naylor reportedly poised to sign a similar agreement with Wigan Athletic.
Meanwhile, Andy Cannon departed at the end of his contract and has been linked with Championship duo Hull and Preston, along with League One pair Charlton and Bolton.
Bryn Morris was unsurprisingly released at the end of his deal, having spent the second half of the campaign on loan at Northampton.