Lambert, 32, underwent a medical examination in Liverpool on Saturday with a view to a move that will reportedly cost an initial �4 million ($6.7 million, 4.9 million euros), rising to �9 million with add-ons.

A former Liverpool trainee, Lambert has emerged as an important squad player for England since scoring against Scotland with his first touch as an international footballer in a friendly last year.

He is a member of the 23-man World Cup squad that will fly to Miami on Sunday for a pre-tournament training camp and Hodgson said that his move to Anfield would be good news for the national side.

"He's very happy. I'm happy for him," Hodgson told reporters after England beat Peru 3-0 in a friendly at Wembley Stadium on Friday.

"I congratulate Liverpool on signing a good player and I'm sure that on Wednesday, when he plays against Ecuador, you'll see a fella running around with all the joy that his heart can muster.

"He's very happy to be here with England and he's very happy that the move has gone through to Liverpool."

Liverpool are also reported to have tabled a �25 million bid for Lambert's Southampton colleague Adam Lallana, who caught the eye against Peru with an enterprising performance.

Luke Shaw is expected to leave Southampton during the close season as well, amid interest from Manchester United, and Hodgson expressed sympathy for the south coast club, who finished eighth in the Premier League.

"It's a pity for Southampton because they've been terrific this year and I congratulate them enormously," he said.

"But unfortunately there are always bigger fish in the sea and it's hard to keep those bigger fish away sometimes."

- Hodgson laments Rooney 'obsession' -

While Lambert, who hails from Liverpool, is riding the crest of a wave, his fellow forward Wayne Rooney found himself criticised in some quarters after a lacklustre showing against Peru.

The United striker, who is recovering from a groin injury, failed to impress before being withdrawn in the 66th minute.

Instead it was strike partner Daniel Sturridge who took the plaudits for a fine 32nd-minute opener, but Hodgson said that it was unrealistic to expect Rooney to be England's match-winner in every game.

"I think it's a bit sad that the country is so Wayne Rooney-obsessed," he said.

"I don't think Wayne sets himself up to be anything other than a very, very important member of the squad, someone who does his best and tries his best at all times.

"As far as I'm concerned, talk about combinations doesn't interest me. All I want is for Wayne Rooney to play well and Daniel Sturridge to play well and to score goals and to create goals.

"That's what they're in the team for and that's what we work hard to help them to do as a team, but certainly we don't have the same obsession with Wayne or Daniel."

He added: "I'm not focusing on one individual. I don't come to press conferences thinking as I walk in, 'What am I going to say about Wayne Rooney or Steven Gerrard today?'

"Steven or Wayne have never asked to be elevated to the position where they are now. They've got there because they're good footballers and they deserve to be there."

After playing Ecuador and Honduras in Miami, England will open their World Cup campaign against Italy in the Brazilian city of Manaus on June 14.

While England's defence essentially picks itself, Hodgson said that the attacking roles in his starting XI were still up for grabs -- suggesting that Rooney's place is far from secure.

"Once you get past Steven Gerrard in the midfield, there's five positions to fill and I think there's quite a lot of options there," he said.