The former Tottenham Hotspur winger has fallen out of favour under manager Zinedine Zidane at the Santiago Bernabeu, but Barnett has ruled out the possibility of the 29-year-old leaving on loan, according to Zinny Boswell at Sky Sports News:
"A loan move is not going to happen. I don't think he wants to go out on loan. He's got a lovely life and home in Spain. I think it would take something exceptional for him to leave and loans are not on the menu. Obviously, Gareth's situation at Real hasn't improved."
Bale's future at Madrid is uncertain after a tough campaign that saw him dropped by Zidane and make just 21 La Liga starts.
The Welshman was left on the bench for Madrid's final match of the season, and Zidane said afterwards he did not know if the 29-year-old would stay:
Madrid have since gone on a spending spree and added to their attacking options. Striker Luka Jovic has arrived from Eintracht Frankfurt, while winger Eden Hazard has been signed from Chelsea.
The duo's arrival will increase the competition for places in the Madrid attack, and it seems as though Bale has been deemed surplus to requirements.
However, finding a buyer for Bale may prove difficult given he is one of Europe's best-paid players:
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Best 5 paid footballers in 2018/19 (pre-tax | inc. wages, bonuses & sponsorship deals): 1 | Lionel Messi (Barça) - €130m 2 | Cristiano Ronaldo (Juventus) - €113m 3 | Neymar (PSG) - €91.5m 4 | Antoine Griezmann (Atleti) - €44m 5 | Gareth Bale (Real Madrid) - €40.2m (FF)
Bale has not spoken publicly about his future, but Barnett said earlier in the season that the forward wants to see out his contract, according to Dermot Corrigan at ESPN FC.
"Gareth has always been clear that he is a Madrid player with three years left on his contract," he said. "He will keep trying [to change the manager's mind]."
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Yet speculation over Bale's future has continued, with Manchester United reportedly set to make an attempt to bring him to Old Trafford on loan, according to Simon Mullock at the Sunday Mirror.
Rumours that Bayern Munich wanted Bale on loan have also been rubbished by Barnett, according to ESPN FC's Adriana Garcia.
Barnett's latest comments suggest that Bale is in no rush to leave the Bernabeu, and if Madrid do want to move him on they will need to find a team willing to take him on a permanent basis.