L'Equipe claim Marseille sporting director Andoni Zubizarreta is getting desperate in his bid to sign a new striker before the end of the month.
The Stade Velodrome club had Bafetimbi Gomis on loan from Swansea last season but stalled on signing him permanently and he joined Galatasaray.
Janssen, who endured a difficult first season in English football following his £17million move from AZ, is now in the French club's sights.
However, Spurs boss Mauricio Pochettino has insisted Janssen is not for sale this summer.
The Dutchman remains his only real like-for-like cover for Harry Kane, although Son Heung-min filled in admirably at times last season.