Smith told the England coach that his priority would not be the friendly against Denmark in Copenhagen on Wednesday but tonight's reserve team match against Bolton Wanderers at the humble County Ground in Leyland, Lancashire.
Eriksson said yesterday that the striker, who would have been the replacement for the injured Andy Johnson, had chosen instead to advance his club prospects after starting United's last two matches on the substitutes' bench.
It is a decision that will no doubt find favour with the United manager Sir Alex Ferguson, rarely a fan of mid-season international friendlies, and it also benefited the Charlton Athletic striker Darren Bent, who capped two goals against Sunderland on Saturday with his first call-up to the England senior team.
Smith's international career has been chequered: although he scored on his debut against Poland almost three years ago, he was sent off in a Euro 2004 qualifier against Macedonia in October 2003 and then had to drop out of a subsequent friendly against Denmark because of an outstanding disciplinary charge.
Smith played six times for England last season, including the World Cup qualifiers against Austria, Wales and Azerbaijan and was on the tour to America at the end of the season. However, Eriksson chose to select Johnson ahead of him and had Peter Crouch been fit it would have been likely that Smith, 24, would also have been behind him.
Eriksson said: "Alan Smith should have been in. But he has played so little football and wants to play in the reserves on Tuesday and have 90 minutes, he told me. So I have Darren Bent from the Under-21 squad coming in.
"If I had to pick my team for the World Cup now, I know the 11 players I would play, if they have a season like last season. But it is a long time between now and May 2006. A lot of things can change, maybe some of them not playing as well as last season."
Bent's goals on Saturday were not his first in the Premiership - that came more than three years ago when he scored the winner for Ipswich against Middlesbrough. Bent established himself the following season with 18 goals and has eight in 12 appearances for the England Under-21.
Asked whether he would consider Chelsea's Jose Mourinho as a successor as England coach, Eriksson, who is contracted until 2008, described the Chelsea manager as a "good organiser and a great motivator. I'm sure he would make a good England manager but I'm not going to resign," Eriksson said. "You have to speak to Brian Barwick about that. I have a contract until 2008. But of course he could be a candidate.
"I've not opened or closed the doors to anybody. I said I thought the FA would choose an Englishman but I don't really know. It's not my problem. I don't know if there are only three realistic candidates [Steve McClaren, Sam Allardyce, Alan Curbishley]. You are asking the wrong person. I want to stay in my job.
"I think there are a lot of candidates. There are a lot of managers in England, English and foreign, who would love to have that job a lot. It is maybe the most prestigious job you can have in the world."
To face Denmark, at the Parken Stadium, Copenhagen, on Wednesday:
David James (Manchester City), Robert Green (Norwich City), Paul Robinson (Tottenham Hotspur).
John Terry (Chelsea), Rio Ferdinand (Manchester United), Jamie Carragher (Liverpool), Matthew Upson (Birmingham City), Gary Neville (Manchester United), Phil Neville (Everton), Ashley Cole (Arsenal), Glen Johnson (Chelsea).
Jermaine Jenas (Newcastle United), David Beckham (Real Madrid), Joe Cole (Chelsea), Frank Lampard (Chelsea), Steven Gerrard (Liverpool), Shaun Wright-Phillips (Chelsea), Michael Carrick (Tottenham Hotspur), Owen Hargreaves (Bayern Munich).
Darren Bent (Charlton Athletic), Michael Owen (Real Madrid), Jermain Defoe (Tottenham Hotspur), Wayne Rooney (Manchester United).
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