The Magpies were understood to have increased their offer for 27-year-old Gomis to £6.9million last week.
However, the Ligue 1 side have been reportedly holding out for a bigger offer for the France international.
Alan Pardew has been eager to increase his attacking options and set his sights on Gomis, who scored 18 goals for Lyon last season.
It is now likely he will turn his attention to bringing in QPR forward Loic Remy, who has been linked with a season-long loan deal.
Shola Ameobi and Papiss Cisse are the club's only recognised strikers and Pardew has been working with chief scout Graham Carr and the club's director of football Joe Kinnear in trying to recruit new talent.