Leeds head coach Marcelo Bielsa reportedly wants to sign Barisic, and the promoted Premier League club made a bid of €9 million (£8.01m) for the Croatia international left-back.
Rangers turned down the English club’s offer for the 27-year-old, according to the report, although it is not clear exactly when Leeds made the bid.
It could have been last month. On August 6, Football Insider reported that Leeds were planning to make a move for Barisic, with Bielsa looking for a new left-back this summer.
Easy decision for Rangers
Barisic is one of the best left-backs in the Scottish Premiership and is a key figure for Rangers.
The left-back has had injury problems and a dip in form during his time at Ibrox, but he remains a brilliant footballer.
Rangers are going strong in the Scottish Premiership at the moment and are planning to stop bitter Old Firm rivals Celtic from making it 10 league titles in a row.
In such a huge season for the club, it is hard to see Rangers sell Barisic, especially for as low an offer as €9 million (£8.01m).