Rams manager Nigel Clough has stated his desire to boost his squad with the temporary signing of a young midfielder from a Premier League club.
The 19-year-old, along with Aston Villa's Barry Bannan who had a loan spell at Pride Park towards the end of last season, is on Derby's list of potential targets.
"Mark Randall is a player we are certainly aware of and he falls into the bracket of the type we are looking to bring in on a long loan," Pearson told the Evening Telegraph.
England Under-18 international Randall is among the crop of talented reserve-team players at Arsenal. He has made 11 first-team appearances for the Gunners, four of them starts, and has played in the Premier League, Champions League and Carling Cup.
Randall, who captained Arsenal's reserves last season, also played 10 games for Burnley in the Championship during a loan spell at Turf Moor in 2008.