Lovenkrands left St James' Park at the end of last season after scoring three goals in 12 Premier League appearances following his arrival in January.
He has yet to find a new team and has recently been training with former club Rangers as he weighs up his options for the coming season.
He was hoping a Premiership club would take him, but so far that has not happened.
However, he could sign for Newcastle (or anyone else) after the transfer window shuts because he is a free agent and not tied to a contract.
Peter Lovenkrands: "Of course I would be interested in coming back to Newcastle.
"I really enjoyed my time at the club and would certainly be interested in hearing what they had to say.
"As far as I know there has been nothing concrete from them although there has been a bit of interest. I have had a few offers from other clubs as well and there are a few things on the table at the moment for me.
"I know Newcastle are a Championship club now, but they still have great fans and I don't think they will be in the Championship for long."