The Reds are said to be keen to get a £53m deal over the line for the France international before he sets off for the World Cup later this weekend.
Reports emerged in the British press on Saturday suggesting that Fekir's big-money switch to Anfield was in jeopardy, however, due to concerns raised during fitness tests this week.
La Graet has moved to play down these fears, though, insisting that the medical - undertaken at Les Blues' national football centre - was a success.
"He's in the middle of negotiations and I think it's done," he is quoted as saying by Goal.com. "I spent 15 minutes with him this morning, and he's worried by the France team. He's in good spirits.
"He passed his medical in Clairefontaine. That's logical, we've done it for other players. He was looking forward to it because the visit he had was positive."
The delay in an official announcement being made is reportedly down to Lyon, who want the deal to go through in the new financial year.
Once the transfer is finalised, Fekir will become Liverpool's second-most expensive signing behind £75m defender Virgil van Dijk.