And Mark Catlin is also hopeful of retaining talented local trio Jack Whatmough, Brandon Haunstrup and Ben Close.
Forde was today released by Millwall at the end of his contract following 339 appearances.
The final year of his deal was spent at Pompey, where he developed into a pivotal figure during the League Two title triumph.
The 37-year-old intimated he would love to return to the south coast on a permanent basis.
Now the Blues have opened negotiations with the free agent.
And Catlin revealed talks with other out-of-contract members of Paul Cook’s squad are also continuing.
Pompey’s chief executive said: ‘We are talking to the agents of David Forde and Noel Hunt.
‘In addition, we continue working on deals for Jack Whatmough, Brandon Haunstrup and Ben Close.
‘Retaining those out-of-contract players has always been our priority.
‘It was important Gareth Evans and Kyle Bennett were signed last week.
‘It ensures we still have the main body of players that did so well this year.
‘Paul also wants to keep some of the younger players like Jack, Ben and Brandon with a view to the club moving forward.
‘We are now going to be very selective on the players we bring in, at all times working diligently within our existing budget.
‘I would like to think we are close to agreements with the younger lads but you really need to speak to their respective agents to see how close we actually are.
‘We have made what we consider to be good offers to them – obviously the ball is in their court now.
‘With those three specifically, they would fall under tribunal laws, so we have an element of protection with them in regards of transfer fees and sell-ons moving forward.’
Pompey have already lost Michael Doyle, Enda Stevens and Liam O’Brien since being crowned champions.
In addition, right-back Calvin Davies has been released.
Unlike last summer when Matt Tubbs, Kyle Naismith and Adam McGurk were transfer listed, there has been no such public statement this time around.
However, Curtis Main is among those with no Fratton future.
Catlin added: ‘No names but there are players Paul feels might be better suited to fulfil their career elsewhere.
‘I am sure Paul will be having discussions with those players over the coming weeks, along with myself and Tony Brown.
‘We are doing all we can to back him in any decisions he takes in regards of players leaving the club.’