Lee travelled to London on Monday to discuss the transfer and Paul says: "We had a very good meeting and when the paperwork is completed - as we are sure it will be - we are confident the deal will be completed in the next 24-48 hours."
And Glenn Roeder underlines that he, too, is confident of a positive outcome, adding: "Everything went well and we expect things to be finalised sooner rather than later.
"This a football opportunity for us to acquire a player who might, in different circumstances, have been beyond what we could afford, so this is a bit of a coup.
"What concerns me is Lee Bowyer as a player. Nothing else is a consideration, and what impresses me about him is that he is self-driven - and I admire self-motivated people who push themselves to the limit.
"He drives himself on and my hope is that he can pull other players along with him and, don't forget, Lee could have perhaps gone somewhere else and played relaxed football - but that isn't his style.
"The best players play better in tougher circumstances, and Lee falls into that category; he is prepared for the challenge, and he is, of course, a West Ham boy."
Former Hammers hero Tony Cottee is delighted by the news of Lee's impending signing, and says: "I'll be well pleased if he signs, to be honest - if we could sign him it would be an excellent one.
"I know he has had problems at different times over the last four or five years but I always like to talk about a player positively, and, as a footballer, there is no questioning his talent or international credentials.
"A couple of years ago he was outstanding in the Champions' League for Leeds - and I think it would be a great coup if we could get him.
"He can become an excellent West Ham player, and I just hope he is not at the club for five months but stays beyond that.
"Lee will obviously want to get back to playing football and away from Leeds where he has had a few problems.
"I understand he was a West Ham fan as a kid and it is always nice to have players who support the club, because they really want to play for you.
"If he can get himself right mentally I really believe he will be an excellent signing."
TC thinks Lee has put his off-field problems behind him and adds: "We all make mistakes in life and sometimes you have to learn the hard way - I think he has done that.
"There weren't too many people willing to take a chance on Paolo Di Canio when he pushed the referee over and, credit to West Ham, they took that chance with Paolo and look how that has turned out.
"Perhaps, in different circumstances, you could say there are clubs that don't want to take Lee Bowyer as a player - but he is an excellent player as well.
"In the past we have been accused of not signing quality players but in Lee we are signing an England international.
"It is a golden opportunity for him and there is no reason, if things go well, to think that Lee won't get back to his top form, help West Ham stay in the Premiership, and get back into the England squad.
"Id like to think it is not just a stopgap signing - it is not as if he is joining a club that has lots of poor players and is definitely going to go down.
"There is a lot of quality - and England internationals - at the club and if we can stay up there is no reason to think Lee can't stay and help us build."
TC hopes there will be more good news soon, and adds: "I think it is a good start to sorting out what the club requires, though I don't think his signing alone will keep us in the Premiership - but if he is the first of a couple that would be good news for the club.
"There is no question that a centre forward is required to relieve the pressure on Jermain Defoe. Fredi has had a lot of injury problems and Paolo is not going to be fit for three or four weeks so we do need someone in.
"Les Ferdinand has been linked and provided he can stay clear of injuries he would be another good signing.
"I just think it is important that whoever West Ham sign it is proven Premiership quality; Lee Bowyer certainly is and so is Les.
"It would be nice to think the club are looking at a centre half to plug the defensive gap as well, though Ian Pearce can drop back to that position, but I can't argue with going for Lee Bowyer."
Tony agrees with Glenn Roeder's policy of looking for British talent and adds: "You are always taking a huge chance if you sign foreign players as they take time to settle."