The 19-year-old is out of contract this summer and also being watched by Premier League giants Tottenham.
Furthermore, Harper and his representatives were present in Scotland on Sunday to witness the Hoops lift the Premiership title.
The English teenager progressed through the youth ranks at the Hawthorns and soon broke into the first-team.
He then spent a short loan spell with Balckburn Rovers and returned to his parent club last year.
As far as this season is concerned, Harper has made 17 appearances in the Championship this season, racking a goal and an assist, mainly as a starter.
However, the talented English teen staggered in the crucial phase of the Championship, eventually receiving stick from the fans for his lacklustre display.
Rakeem has earned 10 caps for the England U-19 side.
Why should the Celts move for Harper?
Harper is a highly talented midfielder, who possesses great physical attributes and a knack of making long-range passes.
A box-to-box player by tradition, the Baggies star can also play in different roles in the middle of the park.
Read more Celtic FC News, click here – Latest Celtic FC News
As the Baggies failed to secure promotion to the Premier League, there are big chances for the Hoops to persuade Harper to move to Celtic Park.