Kante has a history of injuries and missed six months of Chelsea's Premier League season with a hamstring problem.
The Al-Ittihad source said Kante had signed a binding agreement but the club were examining the results of medical tests before agreeing a final deal.
On Tuesday, the Jeddah-based club officially unveiled 35-year-old French Ballon d'Or-winner Karim Benzema as the biggest signing in their history.
"Kante signed a binding agreement, not a final contract," the source said.
"We still review the medical checkup result. He has a long injury history and we want to be careful before signing a huge contract."
Benzema's signing came after Portuguese superstar Cristiano Ronaldo joined Saudi Arabia's Al-Nassr in January in a deal said to be worth more than 400 million euros (£343.3 million).
Benzema and Kante are on a list of around 10 targets who have been contacted by Saudi officials, a source close to the negotiations told AFP last week.
Argentina's Lionel Messi announced on Wednesday he had turned down a blockbuster deal in Saudi Arabia in favour of joining MLS side Inter Miami.
