According to James Benson of the Daily Star, Toffees manager Ronald Koeman will not renew his interest in the France international this winter despite still wanting to strengthen his attack.
Everton are instead set to see how their current squad perform over the next few months and will not pursue the Gunners forward.
Giroud said recently that he did come close to leaving Arsenal in the summer but that he wanted to stay and win more trophies, per Mark Mann-Bryans at The Independent.
The arrival of Alexandre Lacazette from Lyon has increased competition for places up front for Arsenal.
As such, Giroud has yet to manage a Premier League start for the Gunners this season but has featured seven times, per WhoScored.com.
The striker has been a starter in both the Carabao Cup and the UEFA Europa League, and he was on target in the win over BATE Borisov on Thursday.
The goal was a landmark strike by the Frenchman, as noted by Opta:
100 – Olivier Giroud is the 12th fastest player to reach 100 goals for @Arsenal; one game quicker than Robin van Persie. Handsome. https://t.co/QvjTOUAPQR2017-9-28 18:05:51
Despite his reduced role, Giroud remains a key figure for Arsenal. His aerial ability and link-up play add another dimension to the attack, and he is also able to contribute vital goals.
Meanwhile, Inter have played down talk of a move for Ozil, with Ausilio having said he does not expect him to be available, per Premium Sport (h/t Calciomercato.com).
"We are studying our squad, we are scouts everywhere and they look at every kind of player," he said. "I don't think players like him [Ozil] will be leaving in January. Spalletti knows this team has room from improvement; that's what we are working on."
Inter president Erick Thohir had previously said the Serie A side were looking at signing Ozil in January, per Liam Prenderville at the Mirror.
Ozil has been left out of Germany's latest squad for their forthcoming FIFA 2018 World Cup qualifiers due to a knee injury and also missed Sunday's clash with Brighton & Hove Albion with the issue.
Injury data analyst Ben Dinnery described the problem:
Ben Dinnery @BenDinnery
A knee injury will keep Mesut Ozil out this weekends game: "Very short-term. He is not far, but he is not enough for Sunday." #AFC2017-9-29 18:06:51
The German tends to divide supporters due to his languid playing style, but his creativity and ability to provide assists make him a key player.
The club will surely want to keep Ozil, but if he fails to sign a contract extension, they may have to consider selling to avoid him leaving for free next summer.