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FAI general manager Noel Mooney expects Britain and Ireland to mount a "very credible" 2030 World Cup bid.
Group E of the Euro 2020 is made up of Spain, Poland, and Sweden, along with a playoff winner, which will be decided in matches between Bosnia Herzegovina-Northern Ireland and Slovakia-Republic of Ireland.
Wales are hoping to snatch the final automatic qualifying berth for Euro 2020 as they take on Hungary on Tuesday, after the Republic of Ireland were left to settle for a crack at reaching the finals via the play-offs.
The Republic of Ireland missed out on automatic qualification for Euro 2020 as a 1-1 draw with Denmark in Dublin on Monday secured the visitors' place at next summer's showpiece.
Denmark and Switzerland secured spots at Euro 2020 at the expense of the Republic of Ireland on Monday as Roberto Mancini's Italy completed a perfect qualifying campaign by scoring nine.
Despite missing out on automatic qualification, Republic of Ireland boss Mick McCarthy remains convinced they can reach Euro 2020.
Robbie Brady captained the Republic of Ireland to victory over New Zealand, but manager Mick McCarthy says he is not "fully match sharp".
Sean Maguire played a leading role in the Republic of Ireland's win over New Zealand and hopes to be involved against Denmark on Monday.
Ireland manager Mick McCarthy has included Burnley midfielder Robbie Brady and Newcastle defender Ciaran Clark in his squad for the friendly against New Zealand and Euro 2020 qualifier against Denmark.
Republic of Ireland boss Mick McCarthy said he had kept "a close eye" on Aaron Connolly's progress before calling him up to his squad.