After failing to agree fresh terms at the Wham Stadium, the out-of-contract midfielder will now become a free agent and leave John Coleman’s side after two seasons.
A move this close season would also appeal.
Confirming the 24-year-old’s imminent exit, Accy boss Coleman said: ‘Matt has been a good servant to the club and we wish him all the best.
‘We did offer him a new contact but have been unable to offer him an improved contract, so he is now a free agent.’
After leaving Bournemouth in 2020, he amassed 85 appearances for the club - scoring on six occasions.
Any potential move to Pompey would be seen has something of a homecoming.
As a Blues fan, Butcher grew up idolising Matt Taylor while attending Cowplain School and had numerous unsuccessful trials with the Fratton Park while a teenager.
As well as featuring for Bournemouth and Accrington, the midfielder has also played for Gosport Borough, Woking, Yeovil and St Johnstone.