Jefferies left Hearts on Monday just two league matches into the new season after turning down the chance to become the club's Director of Football.
The 43-year-old Paulo Sergio coached Portuguese club Vitoria Guimaraes before joining Sporting Lisbon in 2010 but he quit in February following a poor run of results.
Russian-born Lithuanian businessman Vladimir Romanov became the majority shareholder at Hearts in 2005 and he has appointed a succession of managers who have failed to bring the success he has demanded.
Hearts finished third in the Premier League last season behind Rangers and Celtic, the two clubs who traditionally dominate Scottish football.
The Edinburgh club won the last of their four league titles in 1960.
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.