But it would also lead to the departure of one of Chelsea’s existing three strikers – Fernando Torres, Romelu Lukaku and Demba Ba.
Ba appears most likely to leave, even if only on a temporary basis.
Mourinho said: "I told the players that I want a squad of 22 (players).
"They are professionals. They want to stay. (But) they know that, if somebody’s coming, it will be hard because, normally, somebody has to leave."
The arrival of Willian would also result in a departure, with Chelsea having a host of options for the three attacking midfield positions in which he is earmarked to play.
Victor Moses’ place at Chelsea is most precarious.
Mourinho insists it is not solely his decision on who leaves, whether it is a striker or another forward.
He said: "This is not about choosing one to leave. It’s to agree a situation.
"If a player does not want to leave, the player does not want to leave.
"But we are speaking hypothetically because maybe we don’t get another striker and maybe we keep the three strikers we have."
It was put to Mourinho that Chelsea’s last-gasp pursuit of Willian was designed to unsettle Spurs and was a personal vendetta between the Blues boss and his former staff member Andre Villas-Boas, now Tottenham boss.