The former Rangers striker played with Barton at Newcastle.
Barton was spotted in Glasgow over the weekend, amid reports that he was holding discussions about a potential free transfer switch to the Scottish Championship winners.
Lovenkrands, though, has questioned the seriousness of the 33-year-old's claims and suggested it would not be the end of the world if he were to join the Gers.
"He did mention Celtic when we were together at Newcastle because there were a few Rangers fans in the squad," the Dane told the Scottish Sun.
"Joey never came to any of the Old Firm games with us but he did have a carry on about it, although I am not sure how serious he was.
"Maybe he was a Celtic fan but he wouldn’t be the first to sign for Rangers."
Barton, who was recently named in the Championship's team of the season, is yet to agree a new deal with Burnley despite their return to the Premier League as champions.
Rangers' head of recruitment Frank McParland was instrumental in the Liverpudlian's transfer to Turf Moor a year ago and is reportedly keen on an Ibrox reunion.
Barton, who also played for Manchester City, Marseille and England, would bring some much-needed experience to a youthful Gers squad.