The English newspaper reports that scouts from the two clubs watched the player in action on Tuesday evening as Celtic and Norwich City squared off in a pre-season friendly.
The Kenyan midfielder was previously linked to Liverpool, Stoke and QPR, and he could now leave the Bhoys just one year after joining them from Germinal Berchot.
The 21-year-old arrived to Parkhead in a £900,000 deal from the Belgian side last summer, and he immediately developed into an important player for the Scottish giants.
Victor Wanyama scored 4 goals in 29 Scottish Premier League matches, and has seen his stock rise a great deal following some impressive showings at Celtic.
The promising midfielder is currently rated at £7 million, and the Bhoys may not be able to resist a big money offer that could arrive this summer.