On the departure of Lampard, who has signed a five year deal at Stamford Bridge, Paul revealed: "Although we turned down another bid that may have risen to £12m depending on certain factors, Chelsea's offer was a straight £11m cash, which was a very attractive option to us."
And he has also given details about West Ham's search for Harry Redknapp's successor, denying that an approach was made for Alan Curbishley.
Talking of the money available to Glenn, he says: "Any money received from the sale of Frank plus some other money will give us a transfer budget of around £15-16m for Glenn," he says.
It is, of course, unusual to publicly declare how much money will be available for transfers, but, explaining his decision to do so, he says: "We get asked the question so often so we've decided to reveal the amount, and also because we have been tagged as a selling club - which isn't strictly true.
"If you look at the Deloitte and Touche report you'll see we are a very big net spender on transfers.
"And we want to show our commitment to the supporters. Yes, we have a very big stand going up, but that is being financed by long term money, and doesn't impinge on the transfer budget available.
"And in fact it will be a generator of income very soon, and we are happy to tell supporters that we will be out there in the transfer market trying to buy the right players.
"There are also Bosmans which are perhaps seemingly cheap but you do sometimes have to take wages into account."
"If any of the fringe players are sold, that money will be added to the transfer fund, and Paul adds: "It will reduce the wage budget which will allow us to get the best performers available."
Paul does not envisage, however, that the total number of players in the squad will reduce - but he hopes the strength will increase.
"We all would like to see it improved in quality but to compete with the best I think we do need a squad of the size we have got.
"So we're not looking to reduce the size but we would like to improve the quality."
As for reaction to Glenn Roeder's appointment today, he admits: "We've got many tens of thousands, probably hundreds of thousands of supporters out there, and we've had a number of negative comments.
"It's been a saga that has dragged on possibly a little longer than we would have liked, but we did feel we owed it to everybody to take our time and find the right man.
"It's very difficult to keep supporters involved when you are trying to talk to people in confidence.
"No doubt people will possibly be sceptical but all we - and certainly Glenn - can do is deliver on the football pitch."
Revealing the details for the search for a new boss, he says: "The name everyone spoke about was Steve McClaren and we spoke to him for a few days before it all became public.
"Unfortunately it was put out by a third party that we had been speaking to him; but we were very impressed by Steve and I'm sure he will do very well at Middlesbrough.
"We did speak to a number of people and took a lot of soundings from people we respect within the game, and we spent a lot of time talking with Glenn.
"There was a lot of speculation about who was top of our thoughts and who wasn't but really I think it was overstated in the media about just how far advanced some of our discussions had been with people."
And he insists that no approach was made to Charlton for Alan Curbishley - despite reports.
"We didn't make an official approach for Alan Curbishley - as was very well documented by Charlton they would have refused us permission to talk to him and therefore we were unable to.
"We never sat down and spoke to him but I think Alan made his decision by signing the extension with Charlton and obviously felt that is where he wanted to stay for the next four or five years."
*Glenn has denied rumours that Chris Waddle was a target to be his assistant manager - and reiterated that no announcement on his backroom staff would be made for "a few days."