Upamecano, 21, is regarded as one of the best centre-backs of his age in Europe and was subject of interest from Arsenal during the summer.
RB Leipzig reportedly quoted Arsenal as much as £80million, but the Daily Mail claim the Gunners are ready to make a second approach for the defender.
Arteta has demanded two centre-backs be signed in January amid mounting concerns about Arsenal’s current crop of defenders.
Calum Chambers also appeared to suffer a serious knee injury, which could keep him sidelined for the rest of the campaign.
Club chiefs want to back Arteta in his first window in charge and believe they can convince Leipzig to sell at a knockdown price.
Upamecano has 18 months left on his current deal and Arsenal think they could snap up the Frenchman for just £40m.
After the injury to Chambers, Arteta admitted the club would now re-evaluate their transfer plans for January.
‘We will discuss in the next few days, internally, where we can improve the squad,’ Arteta said after the game. ‘Because at the moment we have a lot of injuries like I said. ‘Some of them might be long term as well, so we have to adapt the plan.