The midfielder is still with the Blues after his arrival at the start of pre-season after leaving Charlton Athletic.
An injury issue put paid to being offered a deal before now, but with the 20-year-old nearing the final stages of his recovery he is hopeful of a full return to training next week.
And that could pave the way to Cowley offering the former West Ham prospect a Fratton future.
Mingi made a good impression with both the Pompey head coach and the rest of the squad before the injury setback.
That slowed his progress, as he attempted to conceal the problem and battle on through pre-season.
Cowley explained he will come to a quick verdict either way once running the rule over Mingi, as and when he makes his return.
He said: ‘Jay’s in the final part of his rehab.
‘He’s on the grass but not with the group, hopefully he’ll be with the group from Monday - and we’ll look to make a call off the back of that.
‘I think we’re open-minded of seeing where he’s at, he certainly did well in those first couple of weeks he was with us.
‘He then picked up the injury, didn’t tell anyone about it and his form tailed off as a consequence.
‘So it’s a good opportunity to have another look at him and then try to make a quick decision, because we’re respectful of his position - you have to also have your heart with the player in these moments.’
Cowley has made 12 signings so far this summer, as he carries out a significant rebuild project after his March arrival.
Among them were Liam Vincent and Jayden Reid with both youngsters few as talents for the future, although Reid unfortunately picked up a serious knee injury in the pre-season warm-up at Luton.
Cowley explained Mingi would be viewed as one for the future, in the way those signings and homegrown Haji Mnoga are.
He added: ‘Jay would be one of those like Jayden Reid, Liam Vincent and Haji. He’s in that group - and he’s a good player.’
A message from the Editor, Mark Waldron
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