Neil Lennon has been heavily involved in talks with the Premier League outfit, as the Hoops consider launching a formal summer bid.
Celtic are open to signing Ajeti permanently or on a season-long loan, with his current market value reportedly set at around £8million – the same fee the Hammers paid Basel for him last summer.
Ajeti, 23, had a brilliant goalscoring record in two years at the Swiss club, netting 29 times in 58 league games. He has struggled to hit those heights so far for West Ham, featuring only nine times in the Premier League.
Ajeti was keen on a loan move away from the London Stadium in January, but because he had played for Basel and West Ham in the same season his options were severely limited.
Celtic are keen on adding a forward as they could be set to lose star man Odsonne Edouard amid interest from a host of Premier League clubs. There is also speculation around Leigh Griffiths’ future, after he came back from the off-season overweight.
Celtic also interested in Greek stopper
Neil Lennon’s men are also interested in bringing AEK Athens goalkeeper and Greek International Vasílios Bárkas to the club this summer.
AEK reportedly want a fee in the region of €7-8m, but Celtic’s current offer of €3.5m + around €1m in add-ons could be enough to push the deal over the line.
Newly promoted Leeds United are also reportedly interested in the goalkeeper, as are Brentford – who could join Leeds in the top flight next season.