A feeling persists in Rome that Cragnotti will lure Eriksson back to Rome - but not just yet. With two league matches to play, Lazio are chasing a Champions League place under coach Alberto Zaccheroni, appointed just seven months ago.
Zaccheroni won Serie A with AC Milan in 1999 and is contracted to Lazio for a further two years. But there are rumours that Barcelona want him for next season.
If that proved to be the case and England suffer badly in Japan, Eriksson might be tempted to re-think his long-term future.
He values his privacy - he changed all his phone numbers this weekend in response to the coverage of his romantic fling - and is uncomfortable with the media frenzy that accompanied the revelations of his affair with Ulrika Jonsson.
What he must now find difficult is the knowledge that he has become a front-line target for further embarrassment in a society that is increasingly obsessed with the private lives of celebrities.
If he wants a long and happy future here, on his own terms, he knows that he must now start to take greater care with his domestic arrangements.
After all, a successful World Cup followed by a less than daunting European Championship qualifying group could lead to Eriksson and England enjoying a glorious summer in Portugal in 2004.
In the final analysis, the England coach should be judged by results. But he isn't always.