The 22-year-old is being considered by Chelsea after Mauricio Pochettino’s side failed to create any clear second-half chances in the 3-1 defeat to West Ham on Sunday.
Balogun was clinical on loan at Reims last season having scored 21 league goals in 37 matches in France but is open to leaving the Emirates Stadium for Chelsea.
Arsenal are aware of Chelsea’s interest and want around £50million for their striker, who is out of contract in June 2025.
Monaco have already had a £34million bid rejected for Balogun, while Fulham consider him among a shortlist of targets to replace Aleksandar Mitrovic, who joined Al-Hilal over the weekend.
Chelsea are weighing up different types of forwards to improve Mauricio Pochettino’s attack after missing out on Crystal Palace’s Michael Olise, who signed a new four-year contract last week.
Pacy Nottingham Forest forward Brennan Johnson, Ajax attacking midfielder Mohammed Kudus and Lyon winger Bradley Barcola are also being considered.
Pochettino is cautious in his search as he seeks to keep balance in his squad, insisting he still has faith in current strikers Nicolas Jackson and Armando Broja.
Injury problems have, however, caused the club to adjust their plans. Carney Chukwuemeka faces six weeks out having had surgery on his left knee, extending the injury list to eight players.
Star forward Christopher Nkunku is also out for four months after injuring his knee in pre-season, while Broja nears his return from major knee surgery in December. Broja will soon be given an Under-21s match or a behind-closed-doors friendly to step up his recovery.
Speaking after the defeat at the London Stadium, Pochettino revealed his thinking on signing a forward: "It is a difficult situation because we have two strikers in Nkunku and Broja but they are injured.
"It is not easy at this moment to find the right profile. We are in the process of working to see if we can add some players in this area.
"But it is a job that is not easy for the club. For sure, they are working really hard to add some players. If it is not possible, we need to wait until Nkunku and Broja will be ready and we have the help of Mason [Burstow].”
Broja has interest from West Ham, AC Milan and Roma but is keen to fight for his place even if Balogun is signed.