He also wants this offer to come directly from the FA chief executive, Brian Barwick, says the Independent.
With the 12-strong FA board meeting yesterday in Soho Square to discuss the process to replace the sacked head coach, Mourinho has also made clear to friends that even if he received such an offer it does not mean he would accept.
"Obviously he would give an answer but he needs the offer first," one said. "And then he can look at what are the good things and the bad things about taking the job."
Mourinho's camp say his agent Jorge Mendes received two phone calls last Thursday, within hours of McClaren being sacked, from middlemen claiming to be working on behalf of the FA and sounding out candidates. Although Mendes is understood to have recognised one of the figures he did not take the calls seriously and is insisting that he will only deal directly with Barwick.
"Jose wants to see what the offer is," a friend said. "He doesn't want to come out and say 'I'm here and I'm interested'. That is not his style. He knows the fans want him - he wants to know if the FA does. It would be stupid if Jorge did not at least talk with the people, with Mr Barwick. It needs to be direct. A concrete proposal. Until then Jose does not want to say anything or give any explanation.
"It's very clear. Mr Barwick talks to Jorge, says what he wants, what he is offering and Jorge talks to Jose. Nobody else needs to know or be involved and a decision can be made. Jose cannot say now whether he wants the job or not because he doesn't know what the offer is and what the conditions are. If there is contact he will think about it."