Da Cruz, 20, only joined the Serie B side this summer, but has certainly made an impressive impact in Italy, scoring five times in 14 appearances for the mid-table outfit.
Eddy Gnahore (R) of Palermo holds off the challenge from Alessio Da Cruz of Novara
The Mirror reports that Da Cruz has found himself on the radar on a number of Premier League clubs, with the Saints being joined by Arsenal, Brighton and Hove Albion and Swansea City on the list of admirers.
It will be interesting to see whether the interest in the former Ajax academy starlet - who is outscoring former Manchester United striker Federico Macheda this season - intensifies to the point that any of the quartet decide to make a move in January, as his scoring record is impressive but his lack of experience would perhaps make a move something of a gamble for any of the four clubs.
Though Southampton scored four times against Everton at the weekend, there is no question that Mauricio Pellegrino's men need to improve going forward, and could perhaps do with boosting their attacking options in January or next summer.
And while Da Cruz may not be a marquee addition, if the Saints do end up signing him of course, his record this season certainly hints that he could be a decent signing with plenty of potential to get even better during the coming years.