The 25-year-old defender is a free agent following the conclusion on his contract with Lens in France and is keen to win a deal in England.
McClaren has brought in young defender Cyrus Christie from Coventry City over the summer, although right-back Toure would provide some additional experience.
Toure came off the bench in last week's friendly against Notts County and flew with the squad to Austria for their clash against Russian side Zenit St Petersburg.
McClaren is not ruling out a move for the French defender, although the Pride Park outfit could well face competition for the player’s signature.
"We had a good look at Alassane and we liked the boy," McClaren told the Derby Telegraph.
The Paris-born defender, who also qualifies for Ivory Coast, came through the ranks at Toulouse and has spent the past five seasons with Lens.
Lens won promotion to Ligue 1 last season and while they offered him the chance to remain at Stade Felix-Bollaert he is keen on a fresh challenge in England.
UK-based agent Tra Desmond told Sky Sports: "Toure has options in France, but the chance to play in England appeals. There are other clubs interested. We'll see what happens."