"Steve is thinking things through," reveals Paul, "and subject to his views there may be another meeting."
Paul says that Steve comes with just about the best recommendation you can get: the admiration of Sir Alex Ferguson.
"The chairman has spoken to him in the course of our checks to make sure we are looking at the right people, and Sir Alex was the obvious port of call."
But Paul played down any thoughts of Sven-Goran Eriksson having a pivotal role in the club's choice, explaining: "We speak to Sven about many things, not least our players; his name came up in conversation, that's all."
If Steve does decide to join the Hammers, Paul does not envisage a clash of interests with him also being part of the England set-up, and he says: "We would be comfortable with that if Steve felt he could do both jobs.
"Everything we hear about Steve leads us to suggest he could successfully become a No.1; everyone that is close to him has no doubt about it.
"Sir Alex has said he recommended he should be No.1 at Manchester United; you couldn't get any higher praise than that.
"Jim Smith speaks of him in glowing terms; Steve is a very articulate and intelligent man who I don't believe will have a problem stepping up.
"He has strong ideas about how a club should be run."
It is likely that, if he does accept the job, he will bring at least one person in, though that would not necessarily be to the exclusion of existing coaching staff.
There may also be compensation required if Manchester United insist on it.
Whether the new appointment changes Frank Lampard's mind about leaving is unlikely, but his sale would at least give funds to be used for rebuilding.
Paul insists that looking to a person without West Ham credentials is not a problem, saying: "We have a great tradition of the manager having been associated with the player as a club, but the real criteria is to find the very best man.
"It would have been a bonus to carry on that tradition, but the be-all and end-all is to get the right man for this club.
"Although we have spoken to Steve it doesn't necessarily rule anybody else out."