The Football Association has broadened its search for non-English players who can qualify for the national side after the failed attempt to bring Steven N’Zonzi into Sam Allardyce’s team and a shift in thinking brought about by the falling numbers of homegrown players in the Premier League.

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N’Zonzi’s move was blocked by Fifa because the 27-year-old Sevilla midfielder, formerly of Blackburn Rovers and Stoke City, had played for France’s Under-21s seven years ago, but the FA is now investigating whether there might be other players who would become eligible because they have spent five years or longer in English football.

Allardyce is behind the change in attitude while acknowledging it is a “very delicate subject”, with the new England manager pushing for a more open-minded approach, in a similar way to Kevin Pietersen initially breaking into the England cricket team on the back of a four-year qualifying period with Nottinghamshire.

The FA did tentatively look at Adnan Januzaj’s potential availability before the Manchester United player, now on loan at Sunderland, aligned himself to Belgium ahead of Kosovo, Albania, Serbia and Turkey, but the governing body has always been reluctant to investigate the issue too closely when it would inevitably lead to accusations of more qualified English players missing out. Mikel Arteta and Manuel Almunia have also been considered in the past but, again, there was little support for the move within the FA or from the relevant England managers at the time.

Allardyce’s view is different at a time when the percentage of English players in the Premier League has never been lower. Diego Costa has been cited as one example, given the Brazilian striker switched to Spain in 2013 having qualified because of seven years playing in La Liga, and the FA is looking at all age ranges in case there are any up-and-coming players who would soon be eligible but were previously considered out of range.

“Cricket do it, rugby do it, athletics do it,” Allardyce said. “It’s not happening [with N’Zonzi] but we can cover this a bit more if I find another player. We have a department to look at the whole situation in all areas for every [age range] international team.

“It happens in all the other countries and we all know the shortage of English players in the Premier League. I think it is only 31%. If those don’t play on a regular basis and there is another option, then surely, if we are going to win something and that player is of the calibre to force his way into the side, we give him an opportunity.”

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N’Zonzi was born in Colombes, on the edge of Paris, but was signed by Allardyce when he was managing Blackburn in 2009, leading to a transfer to Stoke three years later before the midfielder joined Sevilla 13 months ago. Allardyce had earmarked him as a challenger for Eric Dier’s defensive midfield role, having identified that position as an area of the squad where there was not enough cover, and was willing to call up the Frenchman until Fifa blocked the move.

The FA’s feeling is that England need to move with the times and after failing so dismally in their last few tournaments, culminating in the embarrassment of Roy Hodgson’s team going out of Euro 2016 to Iceland, to start giving themselves the best possible chance of winning something – even if it means potentially having someone in the squad who cannot properly speak the language.

At the same time Allardyce is also keen to find out whether there are players, possibly overseas, he did not previously know about who could qualify because of their parents or grandparents – similar to the Calgary‑born Owen Hargreaves, who went on to win 42 caps and was voted England’s best player in the 2006 World Cup.

The difference is that N’Zonzi’s family is of Congolese descent and there is no other link to England apart from the six years in his career when he was playing in the Premier League. On that basis it was put to Allardyce that the FA would inevitably face criticism if, having made a great play of appointing an Englishman as manager, it started bringing in overseas players to improve the side.

“You could say that but does including a player who qualifies because he has played here long enough give us the opportunity to get together the best squad to win?” he said. “The balance is quite difficult. If that player is top quality... do you pick the best squad to win the World Cup? And if one or two of those are like N’Zonzi, do you do it? Or don’t you, and then you suffer the consequences of not winning it, or not getting to the quarter-finals, and failure?”

Hargreaves found it difficult at first to win over the England supporters but Allardyce hopes fans might be more tolerant in the future. “It’s a very delicate subject,” he said. “I’ll have to see, if I actually do it one day, how it’s perceived across the nation. If he goes out and scores the winner, will it be quite that bad?”

Sam Allardyce on...

Roy Hodgson “I haven’t spoken to Roy. I’ve left him alone because I know how disappointed he will be. At some stage I might give him a call but I would have thought he would be sunning himself somewhere. I would be.”

On himself “The Ron Greenwood Room? The names here inspire me. I am in the Sir Bobby Charlton Suite. Do you think there might be a Sam Allardyce Suite here one day?”

Jack Wilshere “If Jack Wilshere was playing every week for Arsenal he’d be in this squad but unfortunately he isn’t. Game-time for Jack has been few and far between, sadly, and unfortunately for him there have been too many injuries. When he plays every week we’ve seen the contribution he has made to Arsenal, but he is not making that at the moment.”

Andre Gray “He’s not in my plans just yet, but if he continues to score goals I have to consider anyone if they become a goalscorer in the Premier League. Who’s the next man to burst on to the scene? Marcus Rashford is a typical example. If Anthony Martial had not got injured in the warm-up, Rashford might never have played for Manchester United.”

Phil Jones and Chris Smalling “Phil’s had a long list of injuries, which has been a particular problem to his development. That is a great shame for him and a great shame for me, having watched him and nursed him through in his early years (at Blackburn Rovers). Making such an impact on the Premier League in that time, it’s a great shame not to go on to be the number one centre-half for Man United and a big pick for England. He’ll have to try to fight his way in, as will Chris Smalling at Manchester United.”