In an interview with SeatPick, Johnson said, West London could be the ideal destination for the England star, as Mourinho was unwilling to start him.
"Alexander-Arnold must be frustrated with such a limited role this season playing for Real Madrid. Before going to Madrid, he would have planned to establish himself as the starting right-back, but the team brought in a new right-back the summer after he joined, which only made him more frustrated.
"Alexander-Arnold is a top player, and no top player wants to sit on the bench; he wants to play consistently. I think he should be a target for Chelsea in January. I think they could bring him in on loan, which would be perfect for both sides. Chelsea currently needs a right-back, and Alexander-Arnold needs more playing time.
"We've seen how effective he can be in the Premier League, and if Xabi Alonso can help him regain his best form, it would be a great deal that solves Chelsea's problems and gets his career back on track."
Alexander-Arnold, 28, should be starting for Real Madrid at the peak of his career, but he remains on the bench as Real Madrid prepares to face Celta de Vigo after the international break.