Rice, 50, said: "I could never imagine leaving the fabulous job that I have at Highbury but I told Arsene I had to speak to Northern Ireland because it was an honour and a privilege to be asked."
Belfast-born Rice won 49 caps for the Irish but moved to London to join Arsenal as a teenager and was a member of their 1971 league and FA Cup Double-winning side. He also played in five FA Cup finals and captained the 1979 Wembley winners. After a spell at Watford in Graham Taylor's successful team of the 1980s he returned to Highbury as youth coach and reserve-team manager before stepping up to second-in-command when Wenger took over three years ago.
With Rice now out of the running for the Northern Ireland job the clear favourite is the Macclesfield manager, Sammy McIlroy, who has indicated he wants to succeed Lawrie McMenemy. The former Southampton manager quit in October after 20 months in charge.
The Irish Football Association has said its wants the new man in place before Christmas to start preparations for the next friendly international matches in February and March.
The Football League is to counter the possibility of top clubs breaking away to form a second tier of the Premiership with a campaign to raise the profile of the First Division. Fears over the growing financial divide between the top flight and the lower leagues have led to suggestions that some of the bigger clubs could move to create a "Premier League II".
However, the Football League's marketing director, Brian Phillpotts, said there had been no contact between it and the Premier League on the matter. Instead, the Football League plans to develop the First Division and narrow the financial gap between it and the Premiership. The League also intends to deliver a new television deal which will provide a better redistribution of wealth among lower-division clubs.Reuse content