Despite making a number of high-profile additions earlier this year, the Gunners currently sit in 14th position in the Premier League standings.
The Gunners would likely have to reduce the size of their squad if they want to make any further signings at the midway point of the campaign.
However, according to Todofichajes, Arteta has asked club officials to submit a fresh bid to bring in Konate at the start of 2021.
The 21-year-old was linked with Arsenal and other Premier League clubs during the summer after impressing during his club's run to the Champions League semi-finals.
Konate has a contract with Leipzig until 2023, leaving the German side under no pressure to cash in on an established member of their squad.