Ambrose is expected to start for Nigeria when they take on Burkina Faso on Sunday and then faces a long flight back to Scotland.
Lennon, therefore, doubts the defender will be fresh enough for a place in his starting XI as he is unlikely to return to the country until Monday evening at the earliest.
"He seems to think he will be back on Monday evening or the early hours of Tuesday; we will assess him and see how he is," Lennon told reporters. "It's difficult for me to think he will be in a starting position."
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The Hoops have struggled with injuries in recent weeks but Lennon is hopeful that James Forrest, Georgios Samaras, Emilio Izaguirre and Fraser Forster will all be available for the visit of the Serie A champions.
"Forrest is fine, he has had the two scans and he came through all clear so he will be in the squad," the manager confirmed.
"He [Forster] is fine, there is no reaction to his injury and he will be ready for Tuesday.
"They [Samaras and Izaguirre] are rehabilitating very well. I think Emilio will be fine, now we are waiting on Sami and we won't know, maybe until Monday."