Mourinho is keen to bring his fellow Portuguese to London this month and talks have been held with his minders.
For his part, Semedo is weighing up his future at Barca after struggling to nail down a regular start this season.
However, Mundo Deportivo says Barca management do not wish to lose Semedo midway through the season. Barca would consider selling the fullback in June.
The defender’s contract carries a €100m buyout clause.