Barton is on the books of Premier League-bound Burnley at the moment, but his current contract with the Clarets runs out in June 2016.
According to BBC Sport, Rangers have made a move to sign the former Newcastle United star on a free in the summer transfer window.
The Gers, who will play in the Scottish Premiership next season after winning the Scottish Championship title this campaign, showed Barton around the Auchenhowie training ground on Saturday, according to the report.
Former Rangers attacker Lovenkrands, who played with Barton at Newcastle United, has suggested that the club’s (reported) interest in the 33-year-old is a sign of things to come.
“Going for a guy like Joey shows what Rangers’ intentions are and shows just how much they want to achieve next season,” the former Denmark international told The Scottish Sun. “It will be interesting to see what other players they target because that is a big statement.”
Barton is a very good footballer and is also a high-profile figure, and signing him would be a massive statement of intent from Rangers.
The Gers have only just returned to the top flight of Scottish football, and landing someone like Barton would send a clear message to Old Firm rivals Celtic.
The Englishman would not guarantee Rangers that they would be competing for the Scottish Premiership title, but he would certainly enhance their quality and give them more confidence.