Rafa Benitez is determined to land the player and is to make a fresh approach to try and sign the Montenegro international.
Jovetic played in the Premier League previously with Manchester City, and is understood to be hesitant over a potential return to England.
The 27-year-old is contracted to Inter Milan and spent last season out on loan at Sevilla.
Newcastle are not the only Premier League team interested in Jovetic.
Newcastle have had an unsuccessful start to the season, losing both of their opening Premier League games, and last night were dumped out of the Carabao Cup by Nottingham Forest.