Celtic join race to sign out-of-contract midfielder
Both the Daily Record and Daily Mail say that caretaker boss Neil Lennon watched the 19-year-old in action as West Brom battled Aston Villa in the Championship play-offs last week.
It has also been stated that Harper was in attendance at Celtic Park this past Sunday as the Ladbrokes Premiership champions closed their season with a 2-1 win over Hearts.
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Hide AdTottenham Hotspur are also interested in signing the England youth international, who is out of contract next month.
West Brom have tried to get the player tied down to a new deal but has thus far been unsuccessful in their attempts.
Harper has played 23 times for the Baggies this season and previously had a spell on loan at Blackburn Rovers.