The 21-year-old has made just nine appearances in all competitions this season due to a mixture of injury problems and players ahead of him in the attacking areas.
Nelson was initially encouraged by manager Arteta to head out on loan last summer and more recently in the January transfer window, but he instead opted to fight for his place at the club.
“We ended up with a large squad at the end of the transfer market,” Arteta said in January.
“We had a few plans in mind with Reiss. One of them was as well to send him on loan to get more minutes because of the competition we have upfront.
“The reality is he has been really good in training. He wants to stay here. He wants to fight for his place.”
Nelson wasn’t included in the squad to face Newcastle on Sunday and hasn’t played for the first team since the FA Cup victory over Newcastle in January.
“With Reiss I would like to give him more,” said Arteta after the 2-0 win over Steve Bruce’s side.
“He’s a boy who trains really hard, he wants to do extra all the time but it’s very difficult at the moment with the players that we have to fit him.
“I feel sorry that we don’t have other competitions to use him because he deserves more. If he doesn’t play more it’s my fault.”
football.london revealed last month that Greek giants Olympiacos are interested in signing Nelson, with their interest in the England youngster going back as early as last season.
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Bundesliga side Hertha Berlin had previously expressed a desire to sign Nelson earlier on in the campaign.
Nelson, who spent a season on loan at Hoffenheim in 2018/19, has two years left on his current contract which expires in the summer of 2023.