Celtic and West Ham reached an agreement over a loan move recently and Ajeti was scheduled to undergo a medical in Glasgow last week.
But the striker asked Celtic to give him more time to take a call on the move as he wanted to assess other options on his table.
Celtic have been hard at work to ease whatever doubts Ajeti had though and Lennon has intervened for talks on Thursday night.
The Celtic manager tried to sell a move to Parkhead to Ajeti and it has been claimed that Lennon’s intervention has worked.
The striker is now close to agreeing on the terms of a contract with Celtic and is edging towards a move to the Scottish champions.
The negotiations have progressed smoothly and Celtic are expecting to complete a deal to sign Ajeti on loan by the start of next week.
Celtic will also reserve an option to make the move permanent for a fee of £5m at the end of the loan stint.
