Such is Jamaica's desire to employ the now former England coach, who is on a shortlist of five high-calibre candidates, that they may also be willing for him to take up the post on a part-time basis.
The move may sound far-fetched but sources close to the Jamaican Football Association claim their interest is deadly serious and is geared towards ensuring the Caribbean island qualifies for the 2010 World Cup having missed out on the last two tournaments.
Eriksson is high on the shortlist that has been drawn up although, as yet, none of the managers have been made aware of Jamaica's interest. The other coaches who will be targeted include three from this summer's World Cup - Portugal's Luiz Felipe Scolari, Germany's Jürgen Klinsmann and Brazil's Carlos Alberto Parreira. The fifth name is Glenn Hoddle, the former England manager who this week parted company with Wolves.
Jamaica had been set to appoint the former England winger John Barnes following a round of interviews conducted towards the end of the season. But Barnes, who previously had an eight-month stint in charge of Celtic, delayed his decision and things have now moved on, although he still remains in the frame.
It is believed that the Jamaican government has now got involved in the process and is willing to fund the appointment, which has led to the Jamaican Football Federation deciding to approach candidates with more experience.
Jamaica also realise that they need to offer a substantial pay package if they are to attract a big name. The salary that could be on offer would make the coach one of the highest paid in international football.
Jamaica are also set to appoint a seasoned coach to take over the technical brief at the Jamaican Federation and overhaul the organisation from the grass-roots through to the under-21 side.
The "Reggae Boyz" - as Jamaica are known - qualified for the World Cup in France in 1998. They became the first English-speaking Caribbean country to reach the finals and reaped economic - as well as sporting - benefits from being at the tournament. They lost to Croatia and Argentina but beat Japan, with their fans also making a big impression.
However, since then their football fortunes have plummeted and they failed to qualify for Germany. More recently there were two dispiriting friendlies in which the team conceded six times against England and four goals against Ghana.
The drive for a big-name coach has the backing of the Jamaican Prime Minister Portia Simpson Miller, who is also the former sports minister. She is enthusiastically pushing for the move after it was argued that because the next World Cup is in South Africa, there are also strong social and symbolic reasons to make sure Jamaica qualify.
Eriksson is, understandably, the most intriguing name on the list. The Swede and his adviser, Athole Still, are currently looking at his options following the end of his term as England coach. He has been linked with a number of major jobs but with Real Madrid having appointed Fabio Capello, one avenue has already been closed off. Benfica are rumoured to be interested in the Swede, who had a previous stint in charge of the Portuguese club, and he has been linked with the South Africa national team.
Parreira, meanwhile, is almost certain to leave his post with Brazil following their exit from the World Cup at the quarter-finals stage. He has come in for fierce criticism and may be attracted to the Jamaica job.
Klinsmann is an interesting possibility as he has already hinted that he will not stay on with Germany, despite their successes at the tournament. The former Tottenham Hotspur striker has no intention of moving his family from California and although he, too, has been linked with a number of clubs, they would not appear to fit in with his plans. He has already ruled himself out of taking over with the United States.
Scolari's contract with Portugal expires at the end of this month - although the Brazilian is understood to have reached a verbal agreement to extend his deal by another two years.
Hoddle resigned from his job with Wolves over the weekend, after becoming increasingly unhappy with the resources available at the Championship club, and has certainly not got another post lined up.