Arteta's side have already defeated Nuremberg and Ipswich Town in friendly encounters this month and will compete in the Florida Cup against Orlando City and Chelsea on July 20 and 23 respectively.
Arsenal will kick off their United States tour against Everton in the Charm City Match on July 16 and will round off their pre-season with the visit of Sevilla to North London for the Emirates Cup on July 30.
According to The Times, a total of three players will not be on the plane to the United States this week, with Partey, Leno and Balogun set to miss out.
Partey suffered a serious thigh injury at the end of the 2021-22 season, but the Ghana international was fit enough to play 45 minutes of the 5-1 win over Ipswich on July 2.
Partey is understood to be training with the team at London Colney but was absent from the 5-3 win over Nuremberg last Friday, and he will remain in the capital alongside Leno.
The German goalkeeper lost his place in the side to Aaron Ramsdale last season and has now been pushed further down the pecking order following the signing of Matt Turner.
Leno is in talks with Fulham over a £10m move to Craven Cottage, and the report claims that he has been left out of the Gunners' tour squad in order to finalise a switch to Marco Silva's side.
Finally, 21-year-old striker Balogun - who previously represented the United States at Under-18 level before pledging allegiance to England - is expected to head out on loan for the 2022-23 season.
Balogun made the step-up to Premier League football with the Gunners last term, but he only made two appearances in the top flight before being shipped out on loan to Middlesbrough.
The England Under-21 international registered three goals and three assists in 18 outings for Chris Wilder's side, and he is now set to continue his development elsewhere.
Arsenal spent £45m to welcome Gabriel Jesus to the club as their new first-choice striker, while Eddie Nketiah committed himself to a new long-term contract at the club last month.
Following the conclusion of their pre-season fixtures, Arsenal will open the new Premier League campaign against Crystal Palace on August 5 at Selhurst Park.