Giroud, who joined the Gunners in 2012, has admitted he had the chance to join Premier League club Everton during the last transfer window.
Former Toffees manager Ronald Koeman was keen to bolster his attacking options and revealed earlier in the season that Giroud was ‘in the building’ to join.
However, France international Giroud pulled out of the move and Allardyce doubts Everton will revive their interest in the player next month.
‘I wouldn’t have thought [Giroud would move] as he refused to come last time,’ Allardyce, who replaced Koeman at Goodison Park last month, said.
‘As far as I know he doesn’t want to move north of Watford, well his wife doesn’t want to anyway.
‘It’s very important to the wives, believe you me. Normally they are the bosses.’
Everton have struggled in front of goal this season and the club are still seeking a replacement for Romelu Lukaku, who joined Manchester United for £75million last summer.
The Toffees appeared to be heading towards a relegation scrap earlier in the campaign but Allardyce has inspired an upturn in results since his appointment.
After being held to consecutive goalless draws, Everton are ninth in the Premier League on 27 points. They face Bournemouth on Saturday.
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