The France international sparked transfer talk after struggling to hold down a regular starting role in the 2016-17 campaign.
With Alexis Sanchez often favoured in a central striking berth, and with a World Cup to think about in 2018, it was suggested that the 30-year-old could move on.
A return to his homeland was mooted, along with a stay in the Premier League at Goodison Park, but Giroud eventually opted to stay put.
Stoke midfielder Adam has, however, suggested that he may not have reached that decision by himself, telling Radio 5 Live: "I heard his partner [Jennifer] refused the deal.
"The deal was nearly done, he wanted to come, but I heard it was his girlfriend or wife that turned it down."
Giroud announced on his decision to remain with Arsenal: "There was something in my soul and in my heart which told me to stay.
"I've been hesitating because I'm the most happy man when I play and I am on the pitch.
"But I keep the faith and I still believe I can have an important part to play this season in the club and I feel good in my head and also physically.”
He has stepped off the bench in all of Arsenal’s fixtures so far this season, with that run starting in the Community Shield and taking in three Premier League fixtures.
Giroud was then included from the start by his country in a 4-0 World Cup qualifying victory over the Netherlands.