Eriksson also believes Lagerback would adapt his methods to suit the players at his disposal.
Should he be offered the Wales job and accept, Lagerback would become the country's first non-British manager.
On Tuesday, Notts County director of football Sven-Goran Eriksson also ruled himself out of the running to replace Lars Lagerback as Sweden manager.
Lagerback succeeds Shaibu Amodu as coach of the Super Eagles after they finished third at the African Nations Cup in Angola last month.
Heading into their next game in Group B against Greece, Etuhu praised the influence of coach Lars Lagerback, who took over the Super Eagles in February.
Lagerback resigned after failing to qualify Sweden for the 2010 World Cup in South Africa where Nigeria have been grouped with Argentina, Greece and South Korea.
Lagerback began his international managerial career as Sweden Under-21 boss, before taking charge of Sweden B and then becoming assistant coach of the senior national side.
The Dutchman was also linked with the vacant Nigeria coaching role, which subsequently went to former Sweden manager Lars Lagerback, who signed a five-month contract on Friday.
However, Lagerback soon signed a five-month contract to take charge of Nigeria, leading the Super Eagles to the World Cup where they were knocked out in the first round.
For Sweden, who only needed a draw to advance, it was the first group stage exit at a major tournament since Euro 2000, but coach Lars Lagerback was gracious in defeat.
Sweden then qualified for Euro 2004 reaching the quarter-finals where they lost to the Netherlands and two years later Lagerback took Sweden to their fourth consecutive championship, the first time in their history.
That run of reaching five successive major finals - and his time in charge of Sweden - was halted by failure to qualify for the 2010 World Cup in South Africa and Lagerback tendered his resignation.
Nigeria's preparations for this tournament have been far from ideal, with Swede Lars Lagerback effectively given only three weeks to prepare his squad for the tournament after replacing Shaibu Amodu as coach and star midfielder John Mikel Obi ruled out with a knee injury but they remained committed to the cause throughout.
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