Mustafi, who currently plays for Valencia, has a £42 million ($55 million) release clause in his contract. But Sky says Arsenal is looking to nab him for just £25.3 million ($33 million) - plus £8.4 million ($11 million) in add-ons.
In football transfers, add-ons can include payments in instalments or royalties on a future sale.
Mustafi is back in Spain, training with his Valencia team-mates following Euro 2016, where Germany went out in the semi-finals to France. Mustafi's agent is expected to fly over to the club shortly to negotiate the transfer fee.
The 24-year-old would complement Arsenal's defence, an area manager Arsene Wenger recently said he needed to bulk up following Per Mertesacker's injury.
Arsenal has been relatively quiet during the summer transfer window. Borussia Monchengladbach's Granit Xhaka is the club's only major signing, for £34 million.
The club's chief executive Ivan Gazidis said this week that despite the club's success - it came second in the last Premier League - it had to be prudent with its signings, saying "we can't afford to outgun competitors that have far more money to splurge on transfer fees than we do. So we have to be very careful, very selective about how we do things."
Arsenal's 2016/17 Premier League season kicks off against Liverpool on August 14.