The Sunday Mail says Wenger was impressed with the 25-year-old midfielder when he took in Alex McLeish's side defeat France 1-0 in Paris last month.
Pearson came on for the injured Darren Fletcher early on and played a major part in the victory. He also played well for Derby in a 6-0 Premiership defeat at the Emirates.
He joined Derby last season from Celtic in a £700,000 deal and helped County win promotion.
Wenger has instructed his scouts to make further checks on Pearo, known for his box-to-box runs from central midfield, and is willing to fork out £1.75million to sign the Scot in January.
Wenger said: "I was impressed with Pearson in the France game. He has also caught the eye playing for Derby."