19-year-old James has enjoyed a breakthrough season at Stamford Bridge, having accumulated 23 first-team appearances.
Liverpool star Alexander-Arnold is also enjoying a terrific campaign, but Cole thinks James has the defensive attributes to challenge the 22-year-old.
The former Chelsea and England midfielder told BT Sport: "He's different class, Reece, people talk about his delivery but he's very rarely out of position defensively, he's a strong lad, he's cold, he's calculated in his play.
"He's been one of Chelsea's most consistent players over the last few weeks. He's going to be pushing Trent all the way.
"When he gets the ball you feel safe in any position. He just puts balls into the area, it's inviting if you're a striker.
"Maybe there will have to be a system change because this guy could be playing for England very, very soon."