The 25-year-old full-back is currently without a club following his release by Crystal Palace.
Parr has spent the last three years on the books at Selhurst Park, but has been deemed surplus to requirements by Tony Pulis after struggling with injury since the turn of the year.
He is, however, a man former Palace manager Freedman knows well, having been signed by the Scot in 2011, and he could be offered the opportunity to remain in England.
Talks are planned with the Norway international, with Bolton aware of the need to bolster their back line.
Freedman told The Bolton News: “I would be very interested if we can get it done on a free transfer.
“I have worked with Jonathan before at Crystal Palace, he’s a good age, he has experience of the Championship and the Premier League and, most of all, he’s a talented player.
“We don’t have many options at left-back at the moment so if we can get something done on a free, then of course I’d like it to happen.”