Edouard joined the Scottish champions in the previous transfer window on a season-long loan deal and he has already made a positive impression from the few opportunities he has been given.
The former France Under-19 international, who has been with PSG since 2011, has scored four goals from five league outings whilst he has also had two cameo appearances in the Champions League.
Manager Brendan Rodgers is said to be pleased with what he has seen from the 19-year-old forward and the former Liverpool boss is eager to make the temporary move into a permanent one come the summer.
Edouard is also believed to be keen on joining Celtic full-time as he feels there is little chance of breaking into PSG's first-team with Edinson Cavani, Neymar and Kylian Mbappe all ahead of him in the pecking order.
It is claimed an offer around the £3-4million mark could be enough to land the forward.