The Germany international, who has an English father, made the switch from Schalke 04 to White Hart Lane in January, but it has emerged that Spurs' North London rivals had the chance to capture him first.
It is believed that the 22-year-old visited the Gunners' training base at London Colney during the Bundesliga winter break in the 2011-12 campaign.
"He was carrying an injury at the time, which was a factor, but that was not the main reason Arsenal pulled out," a source told Goal.com. "Wenger just didn't quite rate him high enough."
Holtby is expected to line up against Arsenal in the North London derby on Sunday.