Per MailOnline's Jonathan Spencer, the winger has been linked with a departure from the Spanish capital on multiple occasions over the years.
Despite telling Italian outlet Tuttosport that Bale is enjoying life at Real, Barnett could not guarantee his client would stay there (h/t Spencer):
"Gareth is very happy at Real Madrid, but if we're talking about the future then nothing is impossible in the transfer market.
"Ronaldo was an important loss for Real Madrid. Gareth loved playing with Cristiano, but he's happy because he's at a top club.
"It's true that since CR7 arrived the foreign superstars are starting to consider Serie A and start looking at it in a different way compared to the last years."
Bale, 29, was primed to replace Ronaldo as Real's main man after the forward departed for Juventus in the summer, particularly after he scored twice—including a stunning bicycle kick—in last season's UEFA Champions League final.
He has struggled to take over that mantle, though. In 17 appearances this season, he has produced six goals and five assists, with his last strike in La Liga coming on September 1.
As the player best placed to fill some of the void left behind by Ronaldo's departure, he will have been frustrated at his failure to do so.
ESPN FC's Dermot Corrigan gave some insight into Bale's struggles:
The Wales international has been far from Madrid's only underperforming player this season, though, which has left them sixth in La Liga after 13 matches.
While Bale may have spent most of his time in Spain in Ronaldo's shadow, football writer Andrew Gaffney believes the former Tottenham Hotspur man has still been a key figure in their success during his time at the club:
Andrew Gaffney @GaffneyVLC
@realmohamed1 Again, that’s just not true. Quite often people see what they want to see in order to fund their opinion rather than the facts. Without Bale there wouldn’t have been 3 consecutive CL titles, a LaLiga title or CdR. He stood up when CR7 didn’t. Who stands up when Bale doesn’t?
He may not always produce consistently, but few players are more decisive than Bale in clutch moments, as he demonstrated in the Champions League final last season.
Real might not miss him too much on a week-to-week basis if he were to move on—they are used to operating without him anyway given his persistent struggles with injuries—but his contributions in their biggest games would be hard to replace.