As per Daily Record, the striker is high on their list of targets and Lennon could look to sign the player on loan.
West Ham would prefer to sell the player permanently but they are open to a loan move as well. Ajeti has not managed to impress at West Ham since his arrival.
The 23-year-old is has failed to score in his 12 appearances with the club so far.
A move to Celtic could allow him to resurrect his career. The Swiss forward needs to play more often and he could partner Edouard in the attack next season.
Celtic need more attacking depth and if Ajeti can find his form, he could prove to be a superb addition, especially on a loan deal. Ajeti had a superb spell with Basel and he will be desperate to regain that form and confidence.
It will be interesting to see if the Hoops can bring him to Parkhead now. They are thought to be keeping tabs on Ivan Toney and Steven Fletcher as well.
Celtic will be chasing their tenth title in a row next season and they must look to add sufficient depth to their attack this summer.