The Switzerland international has been a decisive figure at Arsenal since his £33m move from Borussia Monchengladbach in 2016.
Xhaka struggled to adapt to the Premier League in his first season to prompt criticism of the 25-year-old.
Arsene Wenger stuck with Xhaka throughout the 2017-18 season and scored three goals in 48 games in all competitions.
The Swiss playmaker signed a new long-term contract in May 2018 despite Unai Emery’s appointment as Wenger’s replacement.
The Spanish head coach signed Lorient teenager Matteo Guendouzi and Sampdoria midfielder Lucas Torreira in the summer.
Torreira had impressed during the World Cup as the summer signing helped Uruguay to reach the quarter-finals in Russia.
Xhaka has started all five of Arsenal’s games in the Premier League, with Torreira still waiting to make his full debut.
Former Irish defender Breen believes Xhaka’s passing ability is keeping the Swiss star in Emery’s first team.
“Ultimately what it comes down to is his stats on the ball,” Breen told Irish radio station Newstalk.
“He is one of the best midfielders for passing the ball into the final third.
“He gets Ozil, Aubameyang an Ramsey on the ball. Off the ball, he doesn’t have the athleticism. He can’t get there. He can’t tackle.”
Xhaka has netted eight times in 99 games in all competitions during his two and half seasons or so.
Arsenal haven’t won the Premier League title since 2003-04 when the Gunners finished the campaign unbeaten.
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