Mr Egal became president in 1993, two years after what had been British Somaliland, until fusion with the independent Republic of Somalia in 1960, broke away from the war-torn country.
The parliament was to meet today to consider the offer which Mr Egal said he made because he did not have the support of members of his government.
But Somalis familiar with the situation say Mr Egal's move may be a ploy to secure his position with even greater powers.
Mr Egal, a former prime minister of Somalia, was re-elected in February. No country recognises Somaliland, which he claims will never be reunited with the rest of the country.
Although its capital, Hargeisa, was largely destroyed by forces loyal to the ousted dictator Mohamed Siad Barre in 1989, Somaliland . is considered the most politically stable part of Somalia.
- AP, Mogadishu