The British newspaper claims that the 26-year-old “likes the idea of a switch to Tyneside”.
Austin has struggled with injuries this season, but he remains one of the best strikers in the Championship.
The former Burnley star has scored 10 goals and created 17 chances in 16 league matches for QPR so far this season.
The Englishman has a pass accuracy of 63% and a shot accuracy of 49%, and has won 53 headers, nine dribbles and 13 tackles.
Austin is very much in demand in the January transfer window, with a number of Premier League clubs interested in him.
According to a report in The Daily Star, Newcastle United and Sunderland want to sign Austin.
Aston Villa are also looking to sign the Rangers star in the January transfer window, claimed The Daily Mail.
The Sun recently that Championship outfit Derby County are interested in the striker (click here to read more), with the British tabloid also claiming interest in Austin from London side Crystal Palace.