Jones, who spent the final months of the 2012/13 campaign at Ewood Park, has been released by Wigan Athletic and dropped into the free agent pool.
Rovers would welcome the opportunity to bring him back into their ranks, but appreciate that the midfielder will have other options to consider.
Bowyer said in the Lancashire Telegraph: "David was excellent for us at the end of the season so we'll see if we can get something sorted.
"We're always hopeful but obviously he will have interest from other clubs."
He added on his transfer plans heading forward: "We are still working on things and hopefully it will hot up in the next couple of weeks.
"We want to get players in who the supporters will be proud to have wearing the shirt."
While looking to bring fresh faces into his squad, Bowyer has also moved to block an approach from Dundee United for Goodwillie.
The striker is out of favour at Rovers but he will not be returning for a second spell at Tannadice unless the terms on offer are improved.
Bowyer added: "The offer is not good enough and there are other clubs interested."