Despite winning four Champions League titles with Real, Bale divides opinion because of a perceived lack of commitment and a poor injury record. He seemed set for a move to Chinese club Jiangsu Suning last year before the deal fell through.
The Welshman, who has scored more than 100 goals for the club, infuriated Real fans as he joked about falling asleep with a protective face mask over his eyes while watching the team's recent 2-0 win over Alaves in Madrid from the stands.
"Gareth's fine. He has two years left on his contract. He likes living in Madrid and he's going nowhere," Barnett told the BBC.
"He is still as good as anyone else in the team," Barnett said, adding that Bale's place in the team was up to manager Zinedine Zidane.
"Of course, there's been interest but there's hardly a club in the world which can afford him. It's a great loss that he's not in the Real Madrid team at the moment but he'll not leave.
"Gareth is not looking to outlast Zidane. Zidane has been very successful. There's no hatred. Zidane just does not want to play him. Gareth trains every day and he trains well."
Barnett said that Bale was keen to represent Wales at next year's European Championship, but ruled out a loan switch to another club for regular game time to remain match fit.
"He always wants to play well for Wales," Barnett said.
"Gareth's one of the best players in the world. The best players in the world do not go out on loan."
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