Eriksson took on the Mexico job after managing Man City
Mexico coach Sven-Goran Eriksson has been given the backing of the Mexican Football Federation after Wednesday's 2-0 defeat by the United States.
BBC Sport understands that Eriksson, 61, is Portsmouth's number one target after Tony Adams was sacked on Monday.
"There's total support for Eriksson because we've a commitment with him to get to South Africa," said MFF president Justino Compean.
Eriksson said: "I want to continue. If I left, I'd be a man with no courage."
Wednesday's match was the first in the six-team league that forms the final stage of the CONCACAF qualifying competition.
The top three will qualify for the 2010 World Cup in South Africa and the fourth-placed team will play off against a South American side for another place in the finals.
Mexico have failed to win in four away games since Eriksson was appointed in June.
Portsmouth keeper David James believes that former England manager Eriksson is exactly the sort of name the club should be pursuing.
"Having a former England manager as manager of Portsmouth I'm sure is something that the fans would never have envisaged," said James.
"Somebody of his calibre would be a tremendous acquisition for us."
Eriksson has been linked with Portsmouth following Adams's, along with ex-Chelsea boss Avram Grant and former Charlton and West Ham manager Alan Curbishley.
Other names in the frame for the Fratton Park role include Croatia coach Slaven Bilic, ex-Sunderland boss Roy Keane and former England managers Terry Venables and Glenn Hoddle.
Portsmouth are 16th in the Premier League table - two places and one point above the relegation zone - and Paul Hart has been put in charge of the first team, starting with Saturday's home game against Manchester City.
Commenting on the club's temporary boss, Pompey chief executive Peter Storrie told the club website: "Paul's a strong character and at the moment I think it needs a strong character.
"The players will give him respect for as long as he's doing it. He's a good guy. He jumped at the chance to do it and I'm sure you'll see quite a steadying hand.
"What we need to do is gel together, work as one, cut out the mistakes and just get going and get a couple of results. We really must do everything we can to make sure we stay in the Premier League."
Eriksson led England at the 2006 World Cup before taking over as Manchester City boss. He only lasted 11 months at Eastlands but was named as Mexico coach just a day after leaving the Premier League club.
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