Although the England midfielder is still away on holiday, the west London club have announced they will begin talks with him as soon as he returns, and Paul says: "We have given Chelsea permission to talk to Frank Lampard after accepting a bid of £11million.
"I understand that he is away on holiday at the moment and due back later on in the week, when he and his agent will begin talks."
Lampard has been the source of constant transfer speculation since declaring his intention to leave the club in the wake of his father's departure, and had been widely expected to join up with his best friend Rio Ferdinand at Leeds United, with Spurs and Aston Villa also reported to have made bids.
Says Paul: "No other clubs have made bids that match our valuation of the player, although there is obviously still a chance that they will now."
Chelsea MD Colin Hutchinson had earlier said: "We have made a bid of £11 million for Frank Lampard and that has been accepted by West Ham. That means we have been given permission to speak to the player.
"It's fair to say he has other options and nothing is going to happen overnight as he is currently on holiday.
"When he returns we will look to sit down with him and find out if he wants to come here. If he does we will try and agree personal terms."