Carlo Jacomuzzi was speaking on an Italian radio station when he made the claim, adding that the Toffees are no longer interested in Duvan Zapata.
Everton were in Italy with a view to secure a move for the Serie A star, but have apparently cooled their interest in the Napoli front man.
Jacomuzzi says they are instead “going to sign Giroud for £20million” as the Gunners finalise a move for Lyon’s Alexandre Lacazette.
Speaking to Radio Crc, the scout dismissed the club’s interest in Zapata, saying: “Not anymore.
“We are going to sign Giroud for £20millon; a bargain compared to the €25million being asked for Zapata.”
Everton, who have already been very busy this transfer window, are keen to strengthen their attack ahead of next season.
Star man Romelu Lukaku is expected to leave before the window slams shut next month, and Ronald Koeman sees Giroud as an adequate replacement for the Belgian.
That said, the Frenchman doesn’t seem overly keen on leaving the Emirates, despite Lacazette’s imminent arrival casting serious doubt on his future.
Speaking to arsenal.com Giroud said: “I won a few titles in my career, that is an important thing, but there is another thing which is important for me.
“And that’s the people [see you as a] loyal warrior on the pitch – that you always give your best for the team.
“And that’s why I want to carry on my good journey at Arsenal and I always want to give my best.
“I would love to win another title, or maybe more until the end of my contract.
“The motivation is here, always doing your best to make your family proud.”