Sven-Goran Eriksson's position as England manager is "not at risk in any way", a senior Football Association source has told the BBC.
In a discussion with a News of the World undercover reporter, Eriksson said he could leave his post if England win the World Cup in June.
But his agent Athole Still accused the newspaper of "disgraceful entrapment".
And Still told BBC Five Live that Eriksson had asked him to see if the FA would extend his contract until 2010.
Speaking on Sportsweek, Still said he could not guarantee that Eriksson would be England coach until his current deal runs out in 2008.
But he said: "If the FA wants him to stay, then he will stay - absolutely.
"In fact, Sven said to me quite recently 'perhaps I've got used to this job, in spite of all the annoyances of it, perhaps you should have a word with (chief executive) Brian Barwick and see if the FA would be interested in my staying until 2010'."
Eriksson, his lawyer Richard Des Voeux and Still met the undercover reporter, posing as a rich Arab, in Dubai to discuss a consultancy role for a new football academy, a trip that was sanctioned by the FA.
During the meeting, Eriksson is said to have suggested he would consider becoming Aston Villa boss if the Arab group succeeded in a possible takeover of the club.
"The people we spoke to said they had a substantial sum of money to invest in a Premiership club," said Still.
"I mentioned Aston Villa and Sunderland. The rest of the conversation was sheer fantasy.
"At no point did Sven say he would not honour his contract with England.
"He did talk about possibly managing Aston Villa because you never know what will happen in football, but it was all hypothetical.
"There were never any negotiations, it was all just fantasising."
Aston Villa have since issued a response, which echoes Still's comments.
The club states: "It was a hypothetical conversation between two independent parties and as such has nothing to do with Aston Villa."
Still also made it clear that Eriksson is disgusted at the timing of events.
"Sven is really angry that they have done this in a World Cup year, " he added.
"I will have to read the article fully before considering whether we will take any further action."
However, the News of the World's chief sports writer Martin Samuel told BBC Five Live he believes the newspaper's actions were justified.
"It was a hypothetical conversation that demonstrates what somebody is prepared to do," he said.
During the discussions in Dubai, Eriksson also suggested he could lure David Beckham back to England if the Villa takeover were to succeed.
Samuel continued: "Sven introduces the possibility of buying Aston Villa into the conversation and then after our reporter mentions David Beckham it's Sven that then takes that conversation onto new levels.
"That is what personally I feel is the most damaging aspect of the whole thing".
The reporter in question, Mazher Mahmood, has a track record of trapping public figures in embarrassing stings.
Among other celebrities caught out by the "Fake Sheikh" are England rugby star Lawrence Dallaglio and the Countess of Wessex.