The German goalkeeper is one of the players said to be available to leave the club this summer as the Gunners look to reshape their squad ahead of the upcoming campaign.
Arsenal have already brought in striker Gabriel Jesus, attacking midfielder Fabio Vieira, winger Marquinhos and goalkeeper Matt Turner.
But in order to make more signings, it has been suggested that the club will need to sell players.
According to CBS Sports, Leno has already agreed personal terms for a move Fulham, with an agreement between the two clubs all that is needed before he can put pen to paper on a deal until 2025.
The report states that Arsenal have rejected an offer worth at least £10m and asked for a fee of around £15m.
Leno lost his place to Aaron Ramsdale early on last season and spent the rest of the season as Arsenal’s Cup goalkeeper.
The Gunners have now signed USA international Turner, who is likely to become the new No.2.
In terms of the other incomings, Jesus has already made an impact having netted twice in a 5-3 pre-season friendly victory over Nurnberg.
Midfielder Vieira, meanwhile, has been carrying a minor injury and is yet to begin full training with his new teammates.
‘It’s a small injury I got with the national team one month ago,’ Vieira told The Athletic.
‘Now I feel really good. I’m not training 100 per cent yet, but I’m running. Day after day, I’m improving. And in a few days, I’ll be back in full training with my team-mates.’
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