Modric has enjoyed a legendary stint with Real, making 498 appearances in all competitions since his arrival in 2012.
As well as 37 goals and 77 assists, a wide array of trophies have been delivered during that period, including three La Liga crowns and five Champions League trophies.
However, there are signs that the 38-year-old is dropping down the pecking order at Los Blancos, a consequence of the recent investment in their midfield.
The veteran has been restricted to four starts and six substitute outings in all competitions, not completing 90 minutes on any occasion.
Only holding a contract until the end of the season, talk has persisted regarding an eventual transfer away to Real at some point over the next 12 months.
Furthermore, Modric himself has acknowledged that he feels frustrated with his ongoing situation at the Spanish giants, an indication that he may soon contemplate his future.
Nevertheless, Sanchez has hinted that the current plan is for the Croatia international to spend the remainder of 2023-24 in Madrid at the very least.
Speaking to GOAL, Sanchez said: "Modric to Saudi in January? There are no negotiations on the part of Saudi League officials to include Luka in January.
"We have no plans about his departure from the team at the present time."
If a transfer to the Saudi Pro League became a possibility, it would be to join one of the four clubs that are controlled by the Public Investment Fund (PIF) in Al-Ittihad, Al-Nassr, Al-Hilal or Al-Ahli.
Modric has also been linked with a transfer to MLS in the past, although such interest has quietened in recent months.
Having been restricted to a 23-minute substitute against Sevilla on Saturday, Modric will hope to feature when Real square off against Braga in the Champions League on Tuesday.