The striker spent the second half of last season on loan at Fratton Park.
After completing a January switch from Cardiff City, Bogle made a decent impact for the Blues.
He netted four goals in 14 appearances as Pompey missed out on League One promotion.
The former Grimsby marksman had his share of injuries on the south coast, however.
Following a hamstring setback and swelling to his knee, a groin complaint ruled Bogle out of the second leg of the play-off semi-final loss to Sunderland.
The 25-year-old has since returned to Cardiff following their relegation from the Premier League and has one year left on his deal at the Welsh side.
Jackett felt Bogle displayed glimpses of his potential at Pompey.
And with the boss wanting to strengthen his striking options ahead of a renewed promotion push next season, he will weigh up whether to swoop for the ex-Wigan man for a second time.
Jackett said: ‘Cardiff have come down into the Championship.
‘For Omar, anyway, we will consider him along with all of the other loans.
‘We’ll see whether it is a possibility or a consideration in terms of Omar coming back and fulfilling the potential that we have seen in him.
‘He had a frustrating couple of injuries – first a niggling hamstring and then a groin injury the last game of the season when he would have played.
‘We were looking for him.
‘There were glimpses in that loan spell and we will consider him now along with all the loan players.
‘But nine and 10 positions I do feel we need to strengthen and add competition.’
Jackett has already stated he wants to freshen up his attacking options during the transfer window.
As it stands, Oli Hawkins and Brett Pitman are Pompey’s only striking options – although the manager sees the latter as someone who can operate in the number 10 position.
As reported by The News, Jackett is targeting Ipswich Town’s Ellis Harrison for a third time.
The Blues were keen last summer before the forward departed Bristol Rovers for Portman Road for £750,000 and renewed their interest in January.
Out-of-contract MK Dons ace Chuks Aneke is also on the Fratton Park boss’ radar.