Mariner pointed out Chelsea is still in London so not only would it be a good move for Giroud but also for his other half.
But, speaking on Friday, Wenger denied that Giroud, who has also now been linked with Chelsea, could be included as a part-exchange makeweight.
The Gunners are not in action this weekend after being knocked out of the FA Cup and next play against bottom-of-the-table Swansea on Tuesday in the Premier League.
The Gunners have up until now signed Henrikh Mkhitaryan from Manchester United and Greek defender Konstantinos Mavropanos during the transfer window while allowing Alexis Sanchez get his move away from the club.
It was thought that the 31-year-old was being used in a cash + player swap deal that would see Borussia Dortmund winger Pierre Emerick Aubameyang head to the Emirates, while Giroud went in the opposite direction.
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"I want Olivier to stay", he said. Maybe some youngsters are loaned but the experienced side of the squad stays the same unless someone comes in'.
"We are not close enough to tell you he will do it, I don't know".
According to Sky Sports' Guillem Balague, the clubs remain at loggerheads on the valuation of the player.
"The player will want Arsenal to sort this out as soon as possible". We have nothing to announce today and at the moment we stay where we are. I am perfectly happy with the players I have.