The pair both stole the headlines when they opened their accounts for the Gunners in Sunday's 2-0 win at Liverpool.
"I like Arsenal's style of football and Santi's as well - I love his style of football, with one or two touches," Podolski told the club's official website.
"We play [well] together and you could see it here - he passed for me for the first goal, I passed to him for the second goal.
"But we are only three matches in. We have 35 matches more so we must keep going."
Arsenal resume their Premier League campaign after the international break when they host Southampton on September 15.