The Spanish club's sporting director has held talks with Tiote's representatives this week, according to La Nueva Espana.
Tiote, out of contract at the end of the season, played in Newcastle's last game, the 1-1 draw against Birmingham City at the weekend.
It is unclear if United will demand a nominal fee for Tiote – who joined the club from FC Twente in 2010 – or simply release him from his contract.
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The 30-year-old was handed his first start of the season against Birmingham City at St James's Park last weekend.
Tiote lasted 65 minutes of the third-round FA Cup tie, which ended 1-1.
The Ivory Coast international is the only player Newcastle manager Rafa Benitez expects to lose in this month's transfer window.
"We don’t want to sell anyone if it’s not necessary," said Benitez. "The only one we are open (to selling) is Cheick.”