The veteran midfielder left Atletico Madrid last month with his contract expiring.
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La Real are now in talks with Witsel about a contract, reports transfer expert Sacha Tavolieri.
Negotiations began soon after Witsel's Atletico deal expired, with La Real management eager to add his versatility to their squad.
However, offers have also arrived from other leagues. The 36 year-old free agent has been approached by Standard Liège, the club where he grew up, as well as clubs in the Saudi Pro League and MLS.
But for the moment, Witsel does favour staying in Spain and LaLiga.