It has also been claimed by the newspaper that Scottish giants Celtic and Rangers have tracked the Scotland Under-16 international midfielder this season.
However, it seems that it is Burnley who have won the race to the signature of the highly-rated Connelly.
Burnley, who were playing in the Premier League last season, are fifth in the Championship at the moment with 34 points from 19 matches, seven points behind leaders Brighton & Hove Albion.
Celtic are currently at the top of the Scottish Premiership table with 39 points from 16 matches, four points clear of second-place Aberdeen, who have played a game more.
Meanwhile, Rangers are three points clear of second-place Hibernian at the top of the Scottish Championship table.