Whether the pair play in the Primera Liga next season remains to be seen but England captain Beckham believes both would thrive in Madrid.

He told Diario AS: “They are great players. I have played with Owen and he is a great player and Vieira is one of the best midfielders in the world. However, we have to respect Liverpool and Arsenal.

“If the players decide to leave, which is what it looks like, then I hope they come to Real Madrid, where they would be very welcome. We would improve a lot with Vieira and Owen and it is a huge help to have players like them and it will clearly make us a lot stronger.

“People have to realise they are two of the best players in the world and they would add quality to any team.”

Beckham had a mixed first season at Madrid – starting well before fading after the winter break – but he admits things have gone well as the club prepare to improve on their disappointing fourth-placed finish last term.

He added: “It’s been a good start to the season. It has been a hard pre-season, but that’s better for me as I need to be strong to perform in the games and so hard training has been useful.

“I hope to be more consistent this season. Last season, I played the best football of my life in the first six months of the campaign, but for various reasons after Christmas, I started to play terribly.

“I had two injuries and an ankle injury and people started talking about my private life, it all had an effect.”

Beckham is now working under former Spain coach Jose Antonio Camacho – a man renowned for placing a huge emphasis on hard work.

“He is a hard coach, but I think that’s good because I am used to working with coaches like that,” the former Manchester United star said.

“Alex Ferguson was also very demanding and that is very good for the team.”