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Goalkeeper Wayne Hennessey will train with Wales ahead of their showdown with England on Thursday.
The Crystal Palace keeper missed Wales' win against Slovakia with a back spasm but boss Chris Coleman confirmed he will return to training on Wednesday.
Danny Ward deputised in Bordeaux as the Liverpool keeper made his first start but Bale thinks Hennessey will be fit.
"Hopefully there will be no reaction [to his back injury] today," Wales boss Chris Coleman said.
Gareth Bale backed his teammate to be fit in time for Thursday's showdown and said his injury was not too severe.
"It's just a minor problem and I'm sure he'll recover in time for the England game," said Real Madrid star Bale.
Hennessey was disappointed to miss the 2-1 win against Slovakia and both he and captain Ashley Williams are expected to be passed fit for Thursday's Pool B encounter with the English.
"It is one of those things where you go from broke to mended in about 24 hours," 29-year-old Hennessey said.
Hennessey suffered a similar spasm before Palace faced Liverpool in the Premier League in March.
"I had one and missed the Liverpool game at home for Crystal Palace," he said.
"So I'll have an injection now and I will probably be back in 24 hours, which sounds crazy."
Ward made his first international start in Bordeaux on Saturday, helping Wales to a 2-1 victory.
Hennessey added, "I thought Danny did really well. It was a big situation for him to come in but I thought he was tremendous."
Meanwhile, Aaron Ramsey says that Wales will focus on themselves and not be too preoccupied about England.
Chris Coleman's side lead Group B after England drew 1-1 with Russia in Marseille.
"They had a faultless [qualifying] campaign," Arsenal midfielder Ramsey said, "They have a lot of good players, who are quite dangerous individually.
"But we will focus on ourselves and what we need to do to try and get something out of the game."
Wales became the first British team to win their opening game at a European Championship with victory over Slovakia.
"We wanted to start off well in this competition and we've managed to do that," Ramsey added.
"We work hard for each other, we have quality going forward and we are ready to take on anybody."