The Academy pair have been identified for bright Fratton Park futures as they maintain their development.
Attacking midfielder Bedford has established himself in the Blues’ reserve team which has reached the Premier League Cup semi-finals.
Similarly, Academy skipper Widdrington has also featured at that level on occasions this season.
Pompey have tabled 12-month deals to the pair as they seek to retain their services.
However, their elevation contrasts with the six youth-team colleagues who will leave the Blues at the end of this season.
Topping the list of those not offered terms is leading scorer Harvey Bradbury, who’s bagged 14 goals in 28 Academy appearances during the campaign.
The striker is currently on work experience with the Hawks and appeared as an 87th minute substitute in Saturday’s 2-0 win over Tonbridge Angels.
Bradbury, the son of former Pompey player Lee, also netted for the reserves in last months’ 3-1 defeat at Bristol City in the Central League Cup.
Others released are Nick Hall, Kyle McDowell, Ousman Saidy, Tommy Scutt and Eddie Wakley.
Goalkeeper Hall last month joined Eastleigh on work experience for the remainder of the campaign to cast their eye over him.
The 17-year-old has made 25 appearances for the Academy, yet senior opportunities are limited with Alex Bass ahead.
Bass, who is contracted until 2018, has spent the majority of the season on loan with Salisbury, although made his Pompey debut in the EFL Cup defeat at Coventry in August.
Hall lined-up for the Academy in Saturday’s 4-0 victory over MK Dons at Furze Lane.
McDowell, a left-back, broke into Northern Ireland’s under-18 development team in February,.
He subsequently featured in a 2-0 defeat to Denmark under-18s.
He has made 26 appearances of the Blues this season, in addition to seven reserve outings.
Saidy is a central defender, Scutt a goal-scoring midfielder and Wakley a centre-back formerly on Wycombe’s books.
Meanwhile, Bedford and Widdrington will become first-year professionals with Pompey after landing their prized contracts.
Bedford, who hails from Poole, has scored eight goals in 24 appearances for Harris’ under-18s this season.
He has also started nine of the reserves’ last 11 fixtures as he continues to impress the Pompey coaching staff with his attacking ability.
Widdrington is a central defender or holding midfielder and the son of former footballer Tommy.
He recently started against both Everton under-23s and Sheffield United under-23s during the ongoing Premier League Cup progress.