O’Brien was one of four players who were recently offered fresh terms by Pompey.
Whereas Reeco Hackett, Michael Jacobs and Sean Raggett have all signed new deals at Fratton Park, the 28-year-old has yet to make a decision regarding his future.
Signed by Portsmouth in the January transfer window on a short-term deal, O’Brien went on to produce some encouraging performances for the club in the second half of the 2021/22 campaign.
With his current contract set to expire at the end of June, O’Brien will become a free-agent if he opts against agreeing fresh terms with Pompey.
Making reference to O’Brien’s current situation, Cowley has suggested that he has been offered a good deal by the club and will be given time to resolve his future.
Speaking to The News, Cowley said: “We’ve made an offer which we perceive to be a good offer to Aiden.
“We can only value people within the framework of the finance we have available and the budget we have available.
“But we have made what we think is a good offer.
“We now just have to see how that unfolds.”
Quiz: 23 things literally every Portsmouth fan should know - But do you?
Cowley later added: “We made Aiden that offer and we’d like him to stay.
“Everyone at the club whether players, supporters or us in the management team would like him to stay.
“But ultimately, it’s got to be right for Aiden and it’s totally his prerogative to find out what the options are available to him, before making an informed decision going forward.”
When you consider that O’Brien did illustrate some real signs of promise for Portsmouth last season, it is hardly a surprise that they want him to stay.
During his career to date, the former Sunderland man has managed to demonstrate that he is more than capable of delivering the goods at this level as he has provided 46 direct goal contributions in the third-tier.
With there being no guarantee that O’Brien will extend his stay at Portsmouth, it could be argued that Cowley may find it beneficial to draft up a list of alternative options.
If O’Brien does commit his future to Pompey and goes on to maintain his consistency during the course of the 2022/23 season, he could potentially help the club launch a push for promotion.