Luis Fernandez has said that he wants a two-year contract extension to lead Israel into the 2014 World Cup qualifiers.
Having failed to steer Israel to a top two finish in the European Championship qualifying campaign, it was expected that Fernandez's contract as manager would not be renewed.
He told Israel FA chairman Avi Luzon that Israel was in a period of transition and wanted to carry on the process.
Fernandez, who earned $400,000 a year during the Euro 2012 campaign in which Israel finished third behind Greece and Croatia, said: "I'm prepared to give up half my salary to continue. I don't think I failed. Avi Luzon hasn't taken a decision yet about the next manager."
Fernandez rejected criticism of his management style from Eyal Berkovic. He said: "Berkovic played abroad and never won anything. I can respect winners but not losers."
The Frenchman also suggested that the role could be too much for Eli Guttman, the former manager of Hapoel Tel Aviv, who is favourite to replace him. "After the heart attack that he had he should not continue in management, "Fernandez said. "Look what happened to Gerard Houllier. He had a heart attack at Liverpool and then had a more serious one at Aston Villa.
"My advice is that if they do not give me the job, Israel should find another foreign manager."