The Reds midfielder spent most of last season on loan with the Championship side, making 39 appearances and establishing himself as a fans' favourite.
The 24-year-old has played only a limited role in Liverpool's pre-season, and Freedman would be delighted to bring him back to the Reebok Stadium if a suitable deal can be thrashed out.
"Jay is a fantastic player, our player of the season, and available," Freedman said. "We'll try our very best to make it happen.
"We've got Financial Fair Play and I've got a responsibility to this football club.
"We've done very well with free transfers. If somebody like Jay comes up and the deal is right for the football club, then yes, we will be looking at that."
Freedman has already signed Alex Baptiste and Marc Tierney on free transfers, while striker Jermaine Beckford has joined from Leicester for an undisclosed fee.