Alexandre Lacazette's £52m arrival this summer has led to persistent speculation whether Giroud will leave Arsenal.
The 30-year-old admitted after Lacazette was signed he was unsure what the future holds for him.
He reportedly wants to wait until the start of the Premier League campaign to see how he fits into Arsene Wenger's first-team plans.
Everton have been monitoring his situation as they continue their search for a striker to lead the line with Romelu Lukaku now at Manchester United.
But The Mirror claim Everton could switch their focus to fellow Arsenal striker Welbeck if Giroud decides to stay.
It is said Everton would need to lodge a bid of £30m for Arsenal to consider selling the England international.
Welbeck has had terrible luck with injuries in the past two season at Arsenal and has scored just 17 goals for the north London club since joining from Manchester United in 2014.
But at 26 years old, Everton will be hoping Welbeck's best years are still ahead of him.
It is reported he could also favour a move back up north as he would be able to return to Manchester where he spent his formative years in the United academy.
