Carlton Cole is reportedly wants to settle his future by next week.
The Bhoys may have signed Nadir Ciftci from Dundee United over the summer, but the departure of Stefan Scepovic to Getafe means that manager Ronny Deila is a striker short.
With the transfer window closed, Celtic are limited to free agents, and Deila has been focusing his efforts on former West Ham ace Cole, who left Upton Park at the end of last season.
The 31-year-old striker has been training with Celtic for around three weeks now, though a slight injury last week has ruled him out of training sessions.
The Scottish Sun report that Cole is expected to return to training on Monday, following the international break, but is set to make an ultimatum over his future.
The report claims that Cole has offers from England and abroad, and whilst he is impressed with the setup at Celtic, he wants a decision to be made by next week - or he will go elsewhere.
The ultimatum from Cole could put pressure on Deila to a contract offer in the coming days, with Celtic certainly lacking a target man who can win aerial battles and hold up play - which is exactly what Cole can bring, should he sign for the Bhoys.