According to the Daily Record, Spurs are willing to listen to loan offers after the midfielder's £13million move to Belgian side Club Brugge is set to fall through despite a deal having been agreed.
However, STV have reported that he won't return to Parkhead.
The Kenyan was sold by Celtic for £12.5million to Southampton 2013 before moving on to White Hart Lane for £11million three years later.
It is understood Neil Lennon prioritised the signings of Fraser Forster and Wanyama this summer with the former already through the door, wearing his former team-mate's old 67 number.
If Celtic are to sign their former midfielder it will be on a loan move with the player on a reported £3.3million-a-year deal.